First, Telex couplers are the remote controlled couplers on some locos. The newer couplers (partly) replacing the Relex ones are called Short couplers.

NEM stands for Norm Europäischer Modellbahnen, simply translated this means Standards for European Model Railroads. There's a list of these NEM's on http://www.miba.de/morop/
But since it's in German here are the descriptions of the NEM 360 and 362

NEM 360: This is a standardcoupler for H0, quite similar to the Relex couplers. This standard only applies for the coupler head, so not for the way it is attached to the car.
NEM 362: This is the standard for the socket ("schacht") of the couplers. Sometimes called KK-Kulisse. (Which has of course nothing to do with strange guys in white dresses... KKK stands for Kurz Kupplungs Kulisse, something like a short couplers socket) On most of Märklins newer not-Hobby material this NEM 362 is used. The couplers compatible to this standard are attached with a connection that looks like the tail of a swallow. I hope you understand what I mean.

(Buying material complying with NEM 362 makes quite sure you can attach Märklin couplers to it)

Ah... Socket... that's the word I was looking for earlier while writing my reply. I called it shafs... OOPS I've edited it.

Very informative!
Thanks for the info.
Stephen(USA)