Photo/photograph

There is no difference in meaning, except that (1) photograph can be either a noun or a verb, but photo can only be a noun, and (2) when it is a noun, photo is simply the short form for photograph and thus more casual.   Photo tends to be used more commonly as a noun in spoken English, whereas photograph is more appropriate for formal, written English.

The most important difference between these words is that photograph can be used as a verb, as well as a noun; photo cannot.  Thus, the following sentences are all correct:

That is a nice photograph of you.

That is a nice photo of you.

Can I photograph you?

Can I take a photo of you?

Can I take a photograph of you?

But Can I photo you? is always incorrect.

I hope this helps.

Even though you didn't ask about it, I would like to take this opportunity to put photobomb out there as a new slang term I first heard to describe President Obama's lovely daughters taking candid photos of themselves together with their parents last week at  the inauguration. Apparently, the meaning is "the insertion of one's self, uninvited, into a photograph being taken."  (For example http://www.huffingtonpost.com/2013/01/21/malia-obama-photobomb_n_2522543.html)

Is this an incredibly new term, or have I missed something?  Methinks it would not be appropriate in formal written English.