You asked about the lingo, it sounds like you know but just in case you don't: the Sizzix dies are about 3/4" thick and usually have black foam; the Sizzlet dies are very thin, with a light grey foam.
The sizzlet dies will fit in the Sizzix machine (with the long metal arm) if you buy a converter. The sizzix dies will NOT fit in the sizzlets machine (small machine with black hand crank).
Oh, and the sizzlet dies also have a cool line of embossing templates. Now if I can just figure out how to get them in the middle of the paper . . .