Personally I don't really care whether the term is disabled people or people with disabilities. I like the reasoning behind "person with disabilities" and it's the term I use myself most of the time, but I just don't think it's important enough to waste time over - more time than the few seconds it took to write this post, anyway.
Healthy really isn't an antonym to disabled though. Some people with disabilities are otherwise healthy, some without a disability are not healthy, especially depending on how you define disabled and healthy. There is, at least, a very very rough benchmark for disabled - something like "needs accommodations in order to access a particular environment or opportunity" - but healthy is completely nebulous and personal.
Differently-abled is one I personally hate. It's well-meaning, and some people with disabilities like it - an old acquaintance who's a wheelchair user was a big advocate of it - but it's denying reality. I can see it applying to some types of autism, perhaps, and maybe some other areas of life, but not being able to walk at all isn't really "differently abled" when the vast majority of the human population over the age of 2 is able to walk. There's nothing wrong with acknowledging you can't do something most people can do - it doesn't mean you're less of a person.
I've been told off, on a different forum that I've now left, for describing myself as disabled or mobility impaired rather than specifically saying what my condition is. But I have more than one, and it's a level of personal information that just is not necessary, especially when I'm talking about, say, access to toilets on the ground floor - it's not like it's only people with my condition that need them, is it?