Tony as a singer don't you consider yourself a musician? Singing is musical. I think you can be a musician without being an entertainer, but you can't be a singer without musical ability.
Now trained musician is another thing, but most great innovative musicians the world has ever known have not always been the most or best trained. IMHO
I think when I say I am an entertainer not a musician I would be closer to the mark if I said my voice was my instrument. And my keyboard is a background.