There are
21 pll's. If you split PLL in two steps (first permute corners, then permute edges) you can divide these PLL's in 3 groups:
Group 0: PLL's that only change edges (H, Ua, Ub, Z). You use these for permuting edges
Group 1: PLL's that swap 2 adjacent corners (Aa, Ab, F, Ga, Gb, Gc, Gd, Ja, Jb, Ra, Rb, T)
Group 2: PLL's that swap 2 opposite corners (E, Na, Nb, V, Y)
For 2 look pll (permute corners, permute edges) you actually need to learn 1 alg from Group 1 and 1 from Group 2 to permute corners. You also need to learn all 4 algs from Group 0 to permute edges.
The reason that you can perform an A-perm (3-cycle) to swap two adjacent edges is because you don't care about the edges. You can easily test this on a 2x2x2. Just do an A-perm and then a U or U' so you can easily see that 2 adjacent corners are swapped. Obviously Swapping just 2 corners isn't really possible on a 3x3x3 but again, you don't care about that because you are performing a corner-only step at that moment