The manosphere is an assortment of online anti-feminist groups that differs in their beliefs and goals.
MRAs believe that men are unfairly treated by society and the legal system; they practice social and political advocacy in an attempt to change things to be, in their view, more favorable for men. They point, for example, to statistics surrounding divorce, workplace safety, mortality, crime and punishment, and other issues.
MGTOW, standing for "men going their own way," is a group of men who caution against marriage or serious relationships with women. They do not want to be liable to any women, believing women demand more value than they are worth. Many but not all believe that MRA activism is a lost cause.
If the thesis of MGTOW is "women aren't worth it," the thesis of pickup artists is "women can be gamed." Pickup artists discuss seducing women and getting to sleep with them, as a skill. They practice and share advice on this front.
Staying with the theme, the thesis of incels would be, "women are too hard to game." Incels are men or boys embittered by the perceived difficulty in finding a sexual partner. In the media, incels are most well known for mass shootings they have been associated with.
Incel stands for "involuntary celibate." Incel communities popularized the "chad vs virgin" meme, and the term "chad" meaning an alpha non-virgin.
Many people who reject feminism, but do not necessarily agree with the above groups, are sometimes called part of the manosphere.