This might come as a surprise to you (in fact, it probably will), but there is more than one way to play pretty much every chord on a guitar.
It might help you to understand what a chord actually IS first.
A chord is the 1st, 3rd, and 5th note of the major scale the chord takes its name from.
Since you are familiar with G, I'll use that as my example.
The first note of the G major scale is G. That's the root note, or the note the chord is named for. The third note is B. And the 5th note is D.
So a G major chord is G,B, and D played together and NO other notes.
"But, cnewshadow, I'm playing all 6 strings, so there are more than 3 notes!"
Nope, look again. The 3rd fret of your low E is sounding a G. The second fret of the A is sounding a B. Then you have the 3 open strings. What strings are those? D, G, and B. All notes found in a G major chord. The 3rd fret of your high E is also sounding a G.
So, when you play all 6 strings with your fingers on those frets you are playing, in order: G, B, D, G, B, G. You're playing all 6 strings, but you're repeating the same 3 notes.
Now, you don't NEED to play the high E for it to be a G major chord. You already have all 3 of the notes you need without it.
So, your tablature is telling you to play a G chord, it just omits the high E string from it. The next chord is Gsus4. Remember how I said a chord is the 1st, 3rd, and 5th note of the scale? Well, I fibbed a little because I didn't want to confuse you with too much at once. You can replace notes in chords with other notes. In this case (Gsus4), we are replacing the 3rd note of the scale with the 4th note. The sus4 means "suspended 4th".
The third one is a G chord as well. Only instead of dropping just the high E, it drops BOTH E strings. That chord is sounding BDGB.
So, to sum it up, there isn't ONE correct way to play a chord. As long as you are sounding all the notes you need to form the chord, it is a correct version of that chord.