Completely interchangeable. Neither has any relevance other than preference of word. I’ve been in bands, and groups and I’ve been in bands that we sometimes referred to as a group or vice versa. Not complicated.
Having said that, a “band” is loosely referred to when the members play instruments. Rarely is a vocals only “group” referred to as a “band”. That would maybe be the only real distinction. But plenty of “bands” are groups...