You got it backwards, the N1K1-J and N1K2-J were versions of the N1K WITHOUT floats. The N1K1 (no -J) float fighter came first (the N1K1-J appears to have been the most-produced type, though).
In the IJN naming scheme an "N" as the first character of an aircraft's designation means it is a float plane fighter.
A = carrier fighter (A5M, A6M)
B = carrier bomber (B5N, B6N, B7A)
D = carrier dive bomber (D3A, D4Y)
G = land based bomber (G3M, G4M, G8N)
H = flying boat (H6K, H8K)
J = land based fighter (J1N,
N = float plane fighter (N1K)
A dash and a letter means that whatever its first letter indicates it was it has been modified to the new role, A6M2-N as a carrier fighter modified to be a float plane fighter and N1K1-J/N1K2-J as a float plane fighter modified to be a land based fighter.