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Hello @subsailor731 ;
It’s interesting that @Kitman mentioned fretting the B string at the first fret. Ok, so the big difference between the 3 and 4 finger G chords is that it leaves your index free. If you fret the high E string on the 1st fret, you have a G7 chord. That’s the most common of your new options with the index free.
However, you can also fret the high E string on the 2nd fret and get a Gmaj7 chord. Very cool chord frequently used by the Eagles, if you’re into their songs.
So now, let’s cover fretting the B string at the 1st fret. That would change the open B to a C. However, you still have a B note in the chord so it’s not a sustain chord. Instead it would be an add chord. But do you add the 4th note or the 11th note? Well, the C note is in the next octave above your G, B, D on the lowest 3 strings, so it would be a Gadd11 chord, or simply G11 where the add is implied. A true G11 chord would also have the 7 note, or an F note.
Also, you can fret the 3rd string on the 2nd fret and get a Gadd9.
So yeah, those are the reasons the 3 finger G chord is used much more often outside of Bluegrass.
MG 😀