There is no difference, you still pay your monthly bills as usual. The only advantages is you can get a new phone provider without paying any cancellation fees since you're no longer on contract. You can also get a new phone for free or at a really low price for a 2 year extension.
When my 2 year contract ended nothing changed. It's like I still had a plan (just payed month to month) until I switched to ATT and didn't have to pay anything. I had Verizon, but I assume it's all the same.