But if you pluck an open string, it will vibrate longer than if you were fingering the note. Anyway, we are both right is some respects. The string doesn't vibrate long because (1) there are no frets which means that your finger will dampen the strings and (2) the strings are shorter, which means that there is less mass vibrating and therefore less energy in the strings.
I only mentioned a bow because some people may not be familiar with pizzicato technique. Most people associate violins with the sound that a violin makes when played with a bow.
And yes, violin necks are MUCH shorter than guitars. I believe they are somewhere around the 13-14" scale. That reinforces number 2 above about the vibrating mass being less. With a guitar, you will have a longer length of string vibrating so there will be more energy to keep the string vibrating longer.