George Orwell contributes an apt quote on the differing and contradicting definitions of Fascism:

...the word ‘Fascism’ is almost entirely meaningless. In conversation, of course, it is used even more wildly than in print. I have heard it applied to farmers, shopkeepers, Social Credit, corporal punishment, fox-hunting, bull-fighting, the 1922 Committee, the 1941 Committee, Kipling, Gandhi, Chiang Kai-Shek, homosexuality, Priestley's broadcasts, Youth Hostels, astrology, women, dogs and I do not know what else.

For fascism itself, especially of the Partito Nazionale Fascista, yes, there were some level of quarrel towards what Fascism was supposed to represent. A lot of this comes from the people that were recruited into the movement, and the background that they came from. The economic approach of Fascism as a amalgamation of leftist and rightest policies brought plenty of conflict initially among the Squadrismo who had joined up with the intention of literally beating the old order away. You can view the evolving 'goals' of Fascism as Mussolini and the party leaders bargained and schemed in order to improve their power base. For many, fascism was meant to be "anticapitalist, antimonarchical, anticlerical, antisocialist, antiparliamentary, and, most especially, antibourgeois," (Tannenbaum) but this immediately put them at odds with the founders of the Fascist movement, who were almost all former revolutionary socialists and syndicalists. The base of the party in 1919 may have seen the movement as a way to beat people with their santo manganello, perform daredevil acts of courage, and overthrow existing order, but by 1921 as chaos and striking had been working its way through Italy alienated students and younger veterans started to join the Fascists as a call to order instead of against it.

It's impossible to look at Mussolini for guidance on what the goals of Fascism were, as until he was secure as il Duce he considered the PNF as nothing more than an instrument towards his own rise to power, and viewed those underneath him with a mixture of suspicion and contempt. Instead we can turn towards the various leaders of the Fascist movement themselves where we see the quarrel that you asked about. Edmondo Rossoni, president of the National Confederation of Fascist Unions during the 1920's wanted the movement to be a champion of Italian labor against employers. Roberto Farinacci, former party secretary, saw the party as the violent Squadrismo and thought Mussolini was too liberal. Giuseppe Bottai saw Fascism as the rise of new cultural elites to lead society, while Alfredo Rocco saw Fascism as a constitutional corporatist state. The only tie that led them to all stick together was the syndicalist nature that they all started in.