Verizon uses CDMA network. This is an old type of network technology that currently only Sprint, Alltell and Verizon use. CDMA technology does not use a chip based phone [SIM card]. Also, Verizon does not allow a phone without the crappy Verizon software to run in their network.
AT&T uses GSM network. This is a relatively new type of technology that only AT&T and T-Mobile use it in the US. GSM technology uses a chip based phone [SIM card]. AT&T allows any phone with any OS to run on their network, which is good for the iPhone as it runs Mac OS X.
Just some corrections to this:
1. CDMA is the newer technology, actually. The first CDMA implementation was in 1995, in Hong Kong (Hutchison Telecom).
2. GSM is the older technology, having started in March, 1991 (Finland, Radiolinja).
3. In the US there are actually quite a number of smaller carriers (Cricket, US Cellular, NTELOS) that use CDMA. CDMA currently has more customers in the US than GSM. And there are about 257 commercial operators in 98 countries that use it. Granted, that's a small amount compared to GSM, but still not irrelevant. Think of CDMA as being the "Apple" of the wireless world, with GSM being the "Microsoft."
One last thing: 3G on GSM networks shares quite a bit in common with CDMA, but it is different
enough to be incompatible. The core mappings, the bandwidth requirements, even the numbering systems used to identify handsets are very different, and there's no way to get even a 3G GSM phone working on a CDMA/EVDO network.
Also: The thing about Verizon allowing non-Verizon handsets on their network is largely a farce. They're allowing it only because someone sued, and they even got around that by allowing only handsets on an "approved" list that is controlled by Verizon. I bet you that list is pretty small.
