1). 20GB has no chrome trim, no memory card reader and no wi-fi. Not manufactured anymore. Has the best backwards compatibility with PS2 games due to Emotion Engine (PS2's CPU) and Graphics Synthesizer (PS2's GPU) installed. Once again this one is not made anymore you can buy it used though.
2). NTSC 60GB has the same backwards compatibility as 20GB version, also has memory card reader and wi-fi. Has a chrome trim. Not manufactured anymore. Once again this one is not made anymore but you can buy it used.
3). 80GB - extended memory, but reduced backwards compatibility with PS2 games, it has only Graphics Synthesizer (PS2's GPU). Around 80-90% of PS2 games can be played. Available only in NTSC regions. (north america)
4). 40GB - can't play PS2 games at all (all PS2 chips were removed), has 2 USBs instead of 4, no memory card reader, has wi-fi. Avalable in black, silver and white colors. White and silver versions are on sale only in Japan. Uses 65nm technology (lower power consumption, other versions use 90nm). Improved cooling system. It's the latest version. 40GB doesn't support SACD (Super Audio Compact Disc). Has no chrome trim. Added self-cleaning function.
5). PAL 60GB - reduced backwards compatibility with PS2 games. it has only Graphics Synthesizer (PS2's GPU). Around 80-85% of PS2 games can be played.
Wi-fi included in all models, except 20GB. PAL is is in Europe.
They are all based on Blu-ray. They all play PS1 games. Apart from the differences listed above - they are the same. You can always upgrade with a regular SATA laptop hardrive from walmart if you ever need more space. They run about $150 for 320 GB which is a lot of memory.
My recommendation: Get the 80GB it is the best deal for the money. Comes with the new dual shock 3 instead of six axis and a copy of MGS4 and they are still in production.