A tone is a single sound/note, but a tune is a progression of notes (like a song - it is also an informal term for song).

"Tune" is also a verb, the act of adjusting an instrument (including the voice) in order to get the individual tones correct (described as being "in tune" or being "out of tune"). So as a state of being, "tune" indicates whether a tone is vibrating the correct harmonic sound or not. As a verb it means the act of getting it so.