must have been the next gen model III, ours had the cassette tape. It took 20 minutes to load a crazy game where you shot down nasty flying asteriks in you "Y" (literally the letter Y) wing fighter!! that was, of course, if you had the volume adjusted correctly.
The ONLY TRS-80 that used cassette tape was the Model I. The Model II had an 8" floppy drive, the Model III had 2 5.25" floppy drives. There WERE no "next gen Model IIIs", the Model I, II, III, and IV were all their own generation.