Move order in the Pirc Defense

The position is the Modern defense not the Pirc. The difference is black leads with 1...d6 and 2...Nf6 before fianchettoing the bishop. I would say that Nc3 allows more aggressive options like playing f4 or Be3, Qd2, f3 and 0-0-0.

There is Pirc, Modern Defense, Tiger and so on. These two moves above can lead to virtually everything including Dragon and KID.

Another that g6 and Bg7 allows that d6 and Nf6 does not is the move 3.c4.  Or does it avoid it?

I actually avoid the pirc and drive the game into a King's Indian (3.f3! g6 4.c4 Bg7 5.Nc3) or Old Indian (3.f3! e5 with no fianchetto by Black.)

It depends on what white wants to play next.

Nc3 is more flexible : to play f4 or f3 later (before moving Ng1), or g3/Nge2.

But Nf3 can enable to play c4 or c3 (which can be played now).

There is also this popular system : 1.e4 g6 2.d4 Bg7 3.Nf3 d6 4.Bc4 Nf6 5.Qe2.

To sum up, its a matter of taste.

However, both can transpose