Close, real close. The W112 was a car built in the late 50's if I recall correctly.

The W signifies sedan such as a W210 ('96 to '02 E-class).
It's a 112 motor. I believe it's a 112.981 variant or later. The 112.961 and earlier motors had a different ignition system (and a few other things).

MB Likes numbers. Those friggin German engineers must engineer everything! It's almost like they're obsessive/compulsive or something.

Mercedes issues engine, transmission, and chassis numbers that look like an old VIN.
112.198.12.058736
112 = type of motor (3.2 liter V6)
981 = engineering variant
12 = automatic tranny (10 for standard)
058736 = sequence number to identify this engine (but I just threw 6 digits at random)

722.6xx.xx.xxxxxx for the transmissions in these ( 5 speed auto)

170.449.12.165540 Chassis number for a 2003 SLK230 Kompressor
170 = SLK model
449 = 2002 or newer 230 Kompressor variant
12 = automatic tranny
165540 = production sequence number

WDBKK49J47A165540 VIN number for above SLK
WDB = World Daimler Benz (most cars except ML, R, G, CLS, and SLR)
KK = SLK model
49 = 2002 or newer 230 Kompressor variant
J = drivetrain layout (if I remember correctly)
4 = check digit
7 = code for year produced
A = Sindelfingen production plant (which is obviously wrong for the SLK but I don't remember what the digit is for Karmann)
165540 = production sequence number