Sure, but in this case they are both implementations of a spec defined by PEPs, so a bit more like gcc vs clang (less tightly bound than those, of course, in design decisions). Neither company is trying to invent a new language here.
See also:
https://github.com/microsoft/pyright/blob/main/docs/mypy-com...
https://htmlpreview.github.io/?https://github.com/python/typ...
Fwiw I think performance and features are kind of intertwined here, since Pyright’s extra speed makes it possible to infer more things that are not easy for mypy, especially in an LSP implementation.
Pyright is very impressive in that second link (conformance check), very much a product of Eric Traut & others dedicating a lot of energy to this single problem.