You are correct, Crookedcreek. S&W advertising (All Model Circular, catalogs and box labels) called it the Combat Masterpiece (whether .38 or .22 caliber). Back in the day, Gun Digest and Shooter's Bible followed the S&W lead on this. Unfortunately, nearly all "collector" books refer to it as a K-22 (or K-38) Combat Masterpiece. We're kind of stuck with that.
Note: after model numbers started, the spec sheet included in the box did say K-22 (or K-38) Combat Masterpiece for some reason. That is the only place it ever occurred in S&W literature, and it may be that is where the inaccurate name came from.
On the 6" units (and later 8 3/8"), the nomenclature was K-22 Masterpiece. Never the K-22 Target Masterpiece (or K-38 or K-32). "Target" was never a part of the name.