I agree we're all a little confused how others use these words. To amplify a little what ripock wrote:
Fingerstyle and fingerpicking can be used interchangeably, although sometimes they have special meanings. In some folk and country guitar circles, fingerpicking can refer to different forms of
pattern picking (like Travis Picking and the picking of John Hurt and Elizabeth Cotton) which may or may not always be keeping the melody going while playing the pattern. However, it seems to me that when talking about playing the ukulele, most people use either fingerstyle or fingerpicking when they want to explain they don't just strum.
Regarding chord-melody, if your playing some chord or part of a chord while you play the melody, it's chord-melody. This includes playing the chord with or without the melody. James Hill takes this further by talking about chords on and off the beat and other techniques to give listeners the impression (perhaps) of more than one ukulele playing and calls it "solo ukulele."
I'm happy there are no ukulele police or judges deciding what's right or wrong with any and every thing about the ukulele, but sometimes I do wish our words were a little more standardized. ... (or I was content to go with the flow) ... and "Hey you kids, get off my lawn!")
ld: