The "a fifth" is a general and can be talked about as any kind of 5th while the "a perfect 5th" is specific. Diatonic vs Chromatic does not matter in either case as intervals are independent of scales. G to D is always a perfect 5th regardless of the context.
Scale degrees are not the same thing as intervals, although in heptatonic scales (7 note scales) they almost always correlate to the letter distance between the two notes. An interval is two measurements : the distance in letter names and the "normalized" distance in semitones. The normalized aspect is just that certain intervals have certain spaces where they are typically found and others where they are not. For example C to Eb is a minor third however if spelled C to D# this interval is then an Augmented second since the interval is "bigger than normal". This answer goes into specifics a little more.This answer goes into specifics a little more.