As an addition to the other answers, here's the frequency spectrum of an open low E string of an electric guitar (a Squier strat with a bridge humbucker), strummed with the fleshy part of the finger, plucked with a fingernail, and picked with a plectrum (a Dunlop Delrin-500 .71mm). I played each note a couple of times and then selected one that sounded representative, and was of somewhat equal volume.
For the attack phase I used the first 250 ms of the note, for the sustain phase I used the part from 1 to 1.5 seconds. The graph shows the level in dB of frequencies from 50 Hz to 15 kHz on a logarithmic scale.
I don't make any claims as to how scientific this is, but it's better than looking at the black body radiation of an incandescent light bulb :-)
I think it's fair to say that there is a clear difference in the spectrum of the plectrum-picked note; the harmonics up to around 10 are of comparable amplitude, whereas in the finger-plucked note the first three harmonics clearly dominate the sound. The frequencies between 1 and 2 kHz are also more prominent, and the troughs around 2.5, 6 and 10 kHz are narrower and they all but disappear in the attack phase.