If I have AT&T, can I use a Verizon iPhone?

I have AT&T and I'm buying an iPhone 4. The phone I'm buying online is a Verizon brand. Can I put my SIM card in and still use it even though I have AT&T?

Verizon phones don't have the interchangeable sims card like att does

No.

You don't have a 'sim' card like older phones used to have. Back then you could slap your SIM in any phone and be up and running.

Your memory card doesn't hold any phone settings - just pics, data, etc. - you will have to take the phone to your service provider - and unless it is one of their phones, they won't activate it.

No. The companies are completely different.