Student version has only one license, i.e. can be installed only on one computer only. The other difference is you need to scan and submit your student card (or any proof that you are currently a student) online before you can get your activation/installation key.
On the other hand, standard version has three licenses, and the activation/installation key is provided.
The software remains the same. Just that whether you want a normal Photoshop CS5.5 (it's the latest by the way) or the Extended version.