Does the Verizon iPhone 4s fit into Otterbox defender iPhone 4 cases?

I have been reading different articles and posts and watching videos all evening, but I still can't get a definite answer. One one hand, I've read that the phone does not fit the case and that the case covers sensors. But on the other hand, the iphone 4s is physically the same as the iphone 4, right?

Here's the info I would like: Does the phone fit the case? If not, what is the difference (I've read that the proximity sensor is slightly off, so how much trouble would that give? Etc.)

I'm getting the phone for my mom and she really wants an Otterbox defender case. Thanks for any help! By helping me, you're helping her.

Yes, they are compatible with iphone 4 and iphone 4s