Some policy proposals of leftists and fascists are superficially similar, but the philosophy behind them is radically different. Fascists are driven by a love of their own people and nation; leftists are driven by a hatred of it. Fascists want to preserve culture and tradition; leftists want to destroy it. A fascist could be convinced that more right-wing economics would be good for his nation; a leftist views economics as fundamental to his worldview and so would only accept right-wing economics by renouncing leftism. A fascist accepts that a meritocratic system will lead to natural inequality; a leftist views inequality as unnatural and unjust.

The similarities look closer from a libertarian frame because both philosophies oppose libertarianism. But this is true of many philosophies opposed to libertarianism; all kinds of centrism, classical liberalism, neoliberalism all support things like minimum wages and progressive income taxes to varying degrees.

I don't think that the definition as "authority, laws and rules I personally don't agree with" is a particularly useful one, but I'll concede that many people do use the term in this way.