The G2 and G3 Barrel nuts are for all of the Non QD family of Templar trunnions.
The only difference between the G2 and G3 Barrel nuts is the material and coatings. They are literally the exact same part outside of that.
G2 barrel nuts are made from 4140 steel and are better if you would rather keep swapping your barrel sets around but weight more.
G3 barrel nuts are made from 7075 aluminum and are better if you do not swap barrels often and want the best performance.