Could different entities have the same handle?
No, having a field and a category group (or a section and a user group etc) share handles isn't dangerous at all.

Being specific and semantic with handles in general can be a huge boon for keeping things easily memorable and templates and other source code readable, though – so for example you might want to have handles like genre (for the category group) and selectedGenres (for the categories field), instead of both using genre. Though technically, both can be named genre, no worries.