"Mexican beans" usually refer to dried pinto beans which have be soaked, seasoned, and simmered. Black beans can be used instead, but recipes calling for "Mexican beans" usually mean pintos.
Yes, either can be used. Think of the purpose of the beans in the recipie and how you want the texture, and choose between the black and pinto beans depending on your preference.
I think a recipe that calls for beans in a recipe that wants mexican beans would be a pinto or a black bean. Chilli beans we use kidney beans, and their colors are red or black.
