In my cultural bubble, handicapped and disabled are used relatively interchangeably, and I'm a native English speaker.

That's one of the reasons I felt it was important to point out. I'm not even sure there is a negative connotation in American English (I have vague recollection that "handicapped parking" is sometimes mentioned in American TV shows). The fact that it's being downvoted to oblivion probably indicates that there is not.

Handicap or handicapped-accessible seems to be widely applied to facilities like parking or restroom facilities. I still sometimes see it used to describe people but disabled appears to be the preferred term in that context.

Speaking as an American.