The whole S-Dee-Kay-thingy numbers can be quite confusing indeed when looking back.
The first thing to understand is that the SdKfz number gave the function, so you had the SdKfz 231 meaning a heavy armoured car and applied to earlier 6x4 AC as well as the 8x8 versions, while the medium range radio versions of both were SdKfz 232. The 231 and 232 versions of both 6 and 8 wheel were almost identical apart from the radio and aerials and likely ammo loads. In ASL terms they would be identical. Ditto more heavily modified long range radio versions of both had the same 263 designation.
So what I suspect you want to figure out is
6 Rad = 6 wheel:
SdKfz 231 (6 rad) = Heavy AC with front engine and 6x4 chassis.
SdKfz 232 (6 rad) = as 231 (6R) with medium range radio and bed frame antenna.
SdKfz 263 (6 rad) = quite similar to 232 (6R) but non rotating turret with MG only and long range radio.
8 Rad:
SdKfz 231 (8 rad) = Heavy AC with rear engine and 8x8 chassis.
SdKfz 232 (8 rad) = as 231 (8R) with medium range radio and bed frame antenna, later replaced with pole antenna
SdKfz 233 = SdKfz 231 (8R) with 7.5 cm KwK 37 (same as early Pz IV) replacing the superstructure roof and turret, open topped.
SdKfz 263 (8 rad) = quite similar to 231 (8R) but heightened superstructure, no turret with MG only and long range radio.
Now the others.
SdKfz 221: MG armed, 4x4 light AC.
SdKfz 222: Though looks like the 221, it is a bigger, new 4x4 design.
SdKfz 223: MG only armed, medium range radio equipped AC using the 222 chassis. Early versions used a folding frame antenna.
Light AC platoons might start with (3?) 221s but re-equipped with 2 x 222 and 1 x 223. Use a 221 for a 223 in ASL.
SdKfz 234: Despite a having a very similar hull to the SdKfz 321 (8 rad) series this was a new design using monocoque construction (no chassis frame), new suspension and a diesel engine.
SdKfz 234/1: The original version with a closed top 2 man turret taken from an experimental tracked recon light tank.
SdKfz 234/2: Armament philosophy reverted to the 222 approach.
SdKfz 234/3: The 234 version of the 233.
SdKfz 234/4: A 234/3 with a PaK 40.
As for SdKfz vs PSW, see jrv's comment.