-ing forms can function as adjectives and nouns - here's an example from Practical English Usage:
- You're smoking too much these days (verb: part of present progressive)
- There was a smoking cigarette end in the ashtray (adjective describing cigarette end)
- Smoking is bad for you (noun: subject of sentence)
The verb/adjective forms are called present participles and the noun form is called a gerund, and yes they look exactly the same. The difference is really in how they're being used - what's their role in the sentence?
Dancing queen could be read two ways I think - either describing a queen as dancing (describing what they're doing, as a verb/adjective form), or as another way of phrasing the queen of dancing, where dancing is a noun form and it's another way of saying the queen of dance.
And dance music and dancing music are really the same thing, I'd argue that dancing music used to be what people would call "music for dancing" in the past. Now dance music is used more as the name of a particular style or genre, but dancing music could still be used to describe music intended for formal dances, or things like salsa and tango.