What's the difference between a PS2 and a PS2 Handheld?

Okay, so I've never really been into sony playstations, but I decided I want to buy a PS2, since the prices seem pretty low. I was looking around online, but I mostly saw PS2 Handhelds and I wasn't exactly sure what it was. Are they the same? Does it matter which one I buy? Do they all play the same PS2 Games? And is there any other information I should know about playstations?