The question contains a misunderstanding: PSP games are UMDs.
PSP games were also sold digitally via the PlayStation Store (PSN). These are downloaded directly to the Memory Stick and require no UMD. The PSP Go (model N1000) has no UMD drive at all and relies entirely on digital downloads.
Summary: PSP games = UMDs (physical) or Digital downloads. UMDs only work in PSP-1000/2000/3000 models.