Are PS2 Serial Numbers Unique for each unit?

Are serial numbers on PS2s unique from each unit?

When I'm talking about serial numbers, I'm not talking about model numbers, like SCHP-77001 or anything like that.

I have a PS2 that I want to exchange because it doesn't read burnt DVD Video like FreeDVDBoot. I ask because I don't want the guy to trick me when switching by giving me the same one while switching.

Thanks!