how fascist was Fascism?

There is no generally recognizable and evocative term to bundle together ultra-right radicalism, and in particular the regime family that emerged in the interwar period, than "fascism." This is unfortunate in two respects. First, scholars (like anyone else) want to use evocative and recognizable terms wherever possible, and so different conceptualizations will converge on the same terminology, resulting in polysemy - a problem that crops up in many contexts. Second, the particular term here derives from a proper noun - the Fascism of Mussolini - which makes it easy to think of that case as the prototypical example, or a central example, and certainly at the least an example of whatever the generic term is used to designate. It pushes those who emphasize the particularity of the Italian case, and its distinctions from other states/movements/ideologies commonly called "fascist," to to deny generality more broadly rather than simply view it as a case that had many of its own particularities. Insofar as "fascism" is taken as the furthest right a modern regime can go, it advises typologies where the Italian case can be included among the most extreme category - such that, if someone classifies Spain during the Franco period was merely traditionalist authoritarianism rather than "fascism," while Hitler's fell into the extreme category of a new kind of dictatorship to be assigned such a term, then it's left as a fait accompli to classify Fascism as fascism and thus to be more naturally grouped with the German than Spanish case.

These are all subtle errors, generally far from fatal to the theories they infect, and careful (that is, less natural) language can and often does keep them in check even more than that. However, I suspect that the effects may be especially pervasive because the way we typically hope to employ constructs in social theorizing - bundles of necessary and sufficient conditions - diverges from how we intuitively employ concepts in everyday life, by clusters of more and less central examples. For instance, taxonomists want a set of necessary and sufficient conditions for something being a "bird," but for the rest of us there's just a "region" of things with robins and sparrows at the center and penguins at the edges. And this is not just a matter of classifying convention but can affect our intuitions about real causality. Some of this is tempered by the fact that the most prominent extreme rightist regime of the period was an entirely separate case, meaning that the Italian case is not the sole central example - one has the advantage of name and the other the advantage of immensity. But this only further centers within the concept some of the unusual features they had in common.

all birds are birds, but some are more bird than otherbirds

So what follows are, first, some features that make Italian Fascism somewhat unusual among regimes, ideologies, and movements most likely to also be classified as fascist, by whatever metric, but most especially common usage among scholars; and then, how I think we might be inclined to broadly taxonomize if "fascist" were not the default word we used.

1. Mussolini was an unusually opportunistic, unprincipled, and ideologically incoherent leader. Oftentimes the supposed ideological "amorphousness" and "incoherence" of fascist ideology is founded in the common mendacity of the two most central fascist movements: Mussolini lied, Hitler lied. But most politicians lie, and if Mussolini and Hitler both lied especially frequently, they did so in ways that are relevantly different for assessing the question of ideological incoherence. The Nazi elite had an extremely "coherent" and elaborate internal ideology, as far as such things go; they simply lied about this as well as well as their long-term plans (though they told the truth to other audiences.) The Fascist elite featured a number of different theorists and absorbed elements of other movements, each with their own more-or-less coherent ideologies, but these cohered with each other only minimally, and there was little concrete long-term agenda. Its component tendencies were bound together by the lowest common ideological denominator of nationalism, but what this could mean varied. Other ultra-nationalist movements tended to have a more concrete and inflexible set of proposals about what their nationalism would mean.
2. Italian Fascism was unusually "aesthetically" modernist. This point is generally appreciated, but affects how we see the aesthetic sensibilities of "generic fascism," to the extent that we can make generalizations. (In this case I think the effects of the association are actually salutary for the literature, because otherwise we might breezily associate political reaction with aesthetic traditionalism.)
3. Italian Fascism was unusually secularist. This is another feature it shares with the other "central" example. Both make sense in their context - the growth of the Italian and German national states, which nationalists of all stripes naturally hoped to continue, was bound up in a struggle for authority with the Catholic Church; and in neither case was confessional identity a relevant ethnic marker against the most immediate rivals. This is not just a case of the Catholic cases sometimes seen as "traditional dictatorships" muddying the waters - we can see the same in almost all cases where confession was relevant to ethnic identity, from the Ustaše to the Ossewabrandwag to of course the (recognized outlier in the other direction) Iron Guard. (This is another case where I would say that the effects are accidentally salutary, but again, only accidentally.)
4. Italian Fascism was unusually non-racist, at least prior to the late 1930s and if we are restrict ourselves to a more narrow definition of fascism that excludes the Catholic-identified dicatatorships - but as noted above, when scholars seek to distinguish traditional authoritarians from "real" fascists, Fascists of course end up in the latter, while the Catholic dictatorships of the period are generally not. ("Unusually non-racist" here should be by the standards of "normal" liberal European civilization - there was genuine ideological racism towards, for instance, blacks in Ethiopia, but this was nothing to which the Giolittian centre-"left" had not given its stamp of approval for decades. In some respect the Italian commitment to nationalism actually made it less racist than the status quo ex ante, as in its rejection of various ideas which ascribed the underdevelopment of the South to its inherent racial inferiority.)
5. Italian Fascists were usually likely to be ex-leftists, something shared in common with France, but almost nowhere else. If you are Ze'ev Sternhell and take France and Italy as your prime cases, then your tremendously influential thesis writes itself.

Do these tend in any particular direction? It seems to me that - to an extent stemming from (5) and to an extent from "geographic" features, and probably also just as a matter of coincidence - all of these exaggerate the "break" which fascism makes from the political right, more broadly conceived, and the possible commonalities it had with leftist movements. If the generic term for fascism were not taken from the eponymous Italian movement, I suspect that it would be much harder to treat the right-wing status of the general phenomenon as at all contestable - that, rather than denying that fascism is right-wing, your typical center-right disavowal of fascism would condemn it as "extreme," much as center-left social democrats do respecting dirty communists. 

this nonsense is your fault, Benito

Although this particular narrative might not exist if we did not have Italian Fascism as a central example, it is not as if it is the sole or even the dominant narrative. What is dominant, especially among nonspecialists, is to view fascism as a single regime type which has its first, model-providing case in Italian Fascism and spreads thereafter, with of course different adaptations to particular national traditions - and I think this, though it has fewer obvious ideological consequences and depends less on the particular ways in which Italian Fascism is an outlier, is the real legacy of the name-based contagion. 

What is another way to view the kinds of rightist regimes that emerged in the inter-war period? I think it would be most accurate to speak of two distinct waves of regime formation, which could be cumulative or not, consisting of a first wave in the early 20s and a second wave in the mid and late 30s. What features do we see in this first wave?

1. They are typically weak on ideological coherence, drawing on religious, national, or aristocratic loyalties, but without any strong claim about how they will transform society. 
2. The racial elements that will later become prominent are less emphasized - partaking of racism, certainly, but in most cases no more prominently than did liberalism. (The importance of antisemitism would grow over the course of the 1920s in almost all cases, as literature like the Protocols circulated among rightist elites.)
3. They have a clear ideological unity instead around anticommunism, and in a number of cases are established in the immediate consequence of a defeated communist revolution. Networks of demobilized veterans, especially officers, were prominent in their founding.
4. They cooperated with pre-existing liberal and conservative elites, who in many cases maintained a degree of political freedom and ability to debate policies. They also cooperated with the international liberal order, which saw them as a valuable anticommunist development - even though most of the leadership and activists behind them were generally not "doctrinal" liberals.

More can be articulated, but in general, examples of this can be seen in the postwar regime consolidation in Italy, Hungary, Portugal, Spain (the de Rivera regime), Japan, and elsewhere.

By contrast to the first wave, which was a form of non-liberal anti-communism, the second wave can be characterized as distinctively anti-liberal anti-communism, where rejection of the liberal international order led by Britain and the United States opened the door to radical militarization, ethnic cleansing, activist economic policies, and the replacement of prior bourgeois and aristocratic elites by party activists. And this second wave of regime development frequently occurred within regimes that had gone through the first wave, as in the mid-30s radicalization of Japan and Italy.