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Originally Posted by D-Dawn
I've been confused about this at times also.(calling a Gadd5 a G...or a Cadd9 a C)...different sites and books naming the same chords different names...confusing to a noob...Now I am a bit more confused as the fingering I believed to be called Gadd5 you are calling a G6! ARRRGGGGHHH! 
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I can understand your confusion. The second G chord in the poll is just a variation of a G. It can be called G add 5 because the added note on the second string is the five interval. There is no 6 to be found in that chord. From bass to top string the intervals are 1,3,5,1,5,1. Your adding a 5 to the treble part of the chord which is why it sounds so much brighter. Pretty chord isn't it. You could however play a G6 by just playing the top4 strings open giving you the intervals 5,1,3,6.
How can the same chords have different names? The answer is that while the notes stay the same, the intervals change. A simple example is an Am7 chord at the fifth fret.From 4th string to first sting, the intervals are. b7,b3,5,1. which can be barred with one finger. Handy that. The exact same notes in the same place can also be considered a C6 chord From fourth string to first string the intervals are 5,1,3,6.
Naming the chords is a matter of how they fit logically into a tune depending on the key. As you can see, knowing intervals makes understanding this stuff a bit easier. That is one of the many things
Plane Talk will teach you when your ready.
Hope that helps.