Saying it's all roleplay is nice and inclusive and all, but as soon as you break roleplaying down into nuance its going to get exclusive AF again.
Are there playstyle differences among your group(s)? How do you handle the differences?
I think the point being argued is: calling some styles "roleplaying" is going to make some people defensive, since it's not at all uncommon for 'not roleplaying' to used as a way of dismissing playstyles. This usage is out there, and so any exclusive definition will get pushback.
Anywho, to answer the actual questions:
There's obviously a 3-d continuum of "frequency of different types of encounters or scenes in our games", and sometimes this is based on dm style. Some dm's love (including me) running fights so do a lot of that. Some dm's (that I've greatly enjoyed playing with) hate running fights so have very few. And you could say that about any kind of thing that might come up in the game. But plenty of dm's simply vary based on other factors, like who the players and pc's are or where the characters happen to be.
There's also an array of ways to perform one's character at the table: voice acting is the most obvious, but using descriptive prose is also common and popular, and I've seen a couple players who like to sketch stuff. Even something as simple as speaking in the first person counts, although third-person play isn't any less immersive if you talk about the character. If people have internalized the rules of the game, the rules themselves can be performative, since they precisely describe the intended fictional results (although I'll admit there seems to be a cap on how effective this is when used by itself). And there are degrees of each: some people will only do a bit of description, others can write novellas on the fly.
One thing I want to add about performance: Roleplaying is not performance, but performance almost always comes from roleplaying. Performance, in any form, also helps with immersion for yourself and everyone else at the table. And immersion leads to roleplaying. So it's not just acceptable but actually positive to encourage performance of each character at the table. There's good and bad ways to do this, of course, but it's a good goal to have if that's what everyone wants. The good ways to encourage performance are usually about rewarding performance when it does happen, in a way that accounts for differences in skill, but never punishing a lack of it. As more people do it, other players get more comfortable trying it, and if this is encouraged, you'll see more and more, and thus more immersion.
Just don't conflate lack of performance with lack of roleplaying. Roleplaying can happen entirely internally.
As for handling the differences: the same way I handle different houserules. Be as up-front as you can, keep communication open, and accept that compromise must happen for the game to work. Read the room. Don't be a wangrod.