I know that when plucked as in pizzicato, the violin produces a muted sound. However, I was surprised to find out when I checked with my tuner that if I tune my violin by plucking, it seems somewhat flat when I double check it by bowing! So there's this slight discrepancy between the two. why is that? Is the bowed version correct (which I'm assuming) ? If so then why? also, is it true for any instrument when you play it muted?
Many things can enter in. Bow pressure can force a string out of tune. Try this: tune the open string bowed, then play the string with excessively heavy bow pressure. You'll go out of tune.
Depending on the quality of the instrument, the bridge&soundpost setup, and the phases of Jupiter's moons, you may find that a perfectly tuned (bowed) open string will decay slightly out of tune after you remove the bow. The behavior of a freely oscillating string differs from that of a string driven with a bow.
From a physics standpoint, the resonant frequency of a string under tension, for real-world strings (not those infamous massless ones :-) ), can change with amplitude. Add to that the fact that a plucked string is resonating freely, while a bowed string is actually being caught and released by the bowhairs (at a very high rate), and the math gets well-nigh impossible. I fear I don't have any info as to what the magnitudes of these various effects are. Perhaps someone can chime in w/ some references.