Not really, fascism and communism are obviously both "extreme left" ideologies. The differences are really in the details, which do greatly differentiate them, but at their core (in principal) they both strive for the state and it's people to function as a symbiote, both taking care of eachother, as opposed to a power structure that only serves to keep itself in place while skimming off the top. Anywayssssssss
No, the differences are deep and profound, as are the core assumptions and philosophy. I understand how they can seem like they have superficial similarities by those that know nothing about either, but at their core, they are very different.
Just look at your mistaken assumption at the core, that they both strive for the state and it's people to function as a symbiote. This is wrong. The idea of integralism, the view of the nation and the national state as a super-organism, to be organized organically, most often espoused through the idea and state organization of corporatism (literally from the latin corpus, meaning body) is entirely a nationalist and fascist idea, widely discussed in the underlying philosophies of national-socialism, national-syndicalism, and fascism (or rather, their precursors) at the turn of the last century, such as by Rudolf Kjellén in his writings on realpolitik, geopolitics and biopolitics.
Meanwhile, the stated aim of Marxist thought always remain the abolishment of the state through various means. Why this doesn't happen and how communism tends to deal with reality (or fail to deal with it) is an entirely different discussion, but precisely at the core, this is just one major fundamental difference. Fascist ideologies do not seek to abolish the state at all, but consider it an expression of biology and have an evolutionary concept of statemanship rather than revolutionary.
While nationalist thoughts and fascistoid ideas are inherently opposed to dichotomy, they do have a dichotomous relationship to many marxist concepts. Communism is collectivist, while fascism is philosophically individualist, etc.
Fascism has nothing to do with the left-right spectrum anyway. You can be nationalistic as rightwing or leftwing. Just take a look at China. It is a commie country full of nationalistic fucks and is quite willing to use the military and force to get its way.
You are correct in that nationalism isn't right-wing or left-wing, insofar those concepts even have relevant meaning, but your example is flawed. While Chine has patriotic tendencies, they are state-bound, ethnocentric, and/or reactionary/chauvinist in nature, not nationalist.
Nationalism, at it's core, advocates for the creation and maintainance of national states for the good of the concerned members of said nation, a nation being a natural collective of an ethnicity that forms the basis of said nation. While it is arguable that China has this core by default, especially from an outsider's perspective (not acknowledging the various ethnic groups of China and it's regions), it doesn't actually profess anything like this as part of ideology or doctrine, not implicitly or explicitly.
If anything, China has strong imperialist tendencies in that it acknowledges spheres of influence rather than national self-determination, with the sole focus being the artificial entity of the collective chinese as determined by the chinese government, not the people or the folk.