There was a 60GB PlayStation 3 model (CECHA/CECHB, launch "fat" models in Japan/NA). The statement "no 60GB model existed" is incorrect. Here's the actual launch lineup:
The primary difference is hard drive capacity. The 80GB model also often included DualShock 3 (vs Sixaxis), and some bundles offered software PS2 emulation (limited compatibility). The 40GB is the most stripped-down "fat" model—no BC, no card readers, 2 USB ports.
All original "fat" PS3s are vintage hardware (2006–2009). They suffer from YLOD risk, Blu-ray drive failures, and dead CMOS batteries (which kill digital game access). For playing PS3 games, a Slim (CECH-2000+) or Super Slim (CECH-4000+) is far more reliable. For PS2 games, a modded Slim/Super Slim with PS2 Classics Placeholder or a real PS2 is better than hunting a launch 60GB.