With the arrival of the Z4 M Coupe in 2006, many people and even some auto publications have relabeled the 1999-2002 M Coupe the Z3 M Coupe.  This is not technically correct.  While based on the Z3, the name from BMW was simply “M Coupe”.  Before the M Coupe and Roadster arrived, BMW M models of the time were named according to their series (i.e. M3 for the 3-series, M5, M6, etc.).  BMW probably could have named it the MZ or MZ3, but they chose to name it simply "M".  To me this always meant BMW distilled all the M essence into one unique car, and you could choose to have it in coupe or roadster form.  Whether or not that’s what the BMW product planners intended, that's what I like to think :-).

Lately, BMW has been adding the M to the end of the title of its off-series M cars.  For example, X5 M, X6 M, Z4 M.  I assume this is probably because MX5 was already taken by the Mazda Miata and they wanted to be consistent.  They didn’t do that with the 1998-2002 M cars.  While it’s convenient to add the "Z3" for reference, it takes a way some of the specialness of THE "M".