@BeamBrain@hexbear.net is right:

MGTOW is older, I believe mostly GenX and to some extent Boomer, and was "a thing" earlier on where they tried to pass themselves off as a legitimate movement. "Self help for men" type shit. Even trying to influence law to get the courts to grant more rights to fathers in custody cases (which I admit is not 100% always a bad thing). Most of that is a pretense though, and it becomes immediately obvious when you talk to them that they are of course nothing more than flaming misogynists with a persecution complex. Again, they tend to be older so a good percentage of them have been married and divorced, often with grotesque sob stories about how their wives stole everything from them, and now they're struggling triumphantly to reclaim their masculinity or some shit. But it's just usual run of the mill misogyny and anti-feminism.

Incel on the other hand grew entirely out of internet culture, and so never had that earlier GenX-like air of legitimacy. They tend not to have ever had wives or even girlfriends, as one of their defining grievances is that they are virgins, and will remain so for the foreseeable future if not indefinitely. Hence "involuntary celibacy." It's not really a cohesive movement as much as a nebulous, twisted internet subculture with varying degrees of incels tying to make it a movement or coherent ideology. Like most subcultures they have their own terminolgy and sickeningly sexist language but are united really by their extreme hatred of women and a sense of shattered privilege because they suffered the social but very personal crime against them of not by default getting the hot /insert misogynistic slur/ to fuck that society always promised them.

That's how it's been as far as what I've come across anyway.

Edit: But lol, Incels are not stoic. They tend to be extremely whiny and entitled. They have no inner calmness, but a constantly simmering rage against women, and, as this thread and their violent rhetoric and actions makes evident that rage simmers for People of Color too. And often even a more general rage for society itself, but for misogynistic and patriarchal reasons, anything they can twist into being the cause of them being denied their god given right to women's bodies. They are the complete opposite of stoic. The NoFap movement which has some crossover with Incels tries to be stoic in some ways for obvious reasons. And there was crossover because NoFap offered a "cure" of sorts for some portion of Incels. To be clear, NoFap as a movement is also filled with misogyny and has some very weird beliefs bordering on esoteric about super powers and shit like that. But they also come with the generally good and obvious advice that if you are addicted to something, breaking that addiction can be beneficial. Specifically giving up an extreme porn addiction is undoubtedly a positive step for many of these men. But it's only one step among many needed to have any hope of breaking them of their pathologically patriarchal ideology.

I suspect you got the stoic part either from the joke we make of it here about being VolCels, (and fuck yeah we VolCels incorporate Stoicism in keeping our vital fluids to ourselves) or because of the Incel-NoFap venn diagram wedge.