'Snoop' means moving around looking for something. It's an activity. If you are 'snooping around' the suggestion is that you're going somewhere to be nosy. For example: 'We don't want reporters snooping around the college trying to find out what's going on here.' 'Pry' mean to look at something in an intrusive way. For example, we would hide something to keep it away from 'prying eyes'. It can also be verbal. For example, someone might say 'I don't mean to pry, but I couldn't help noticing that...' and then they would proceed to ask you something about your personal life.

"My boss keeps asking me about my family. It was nice at first but now I feel he is prying into my personal affairs." "If you want to know about my friends, just ask me, but don't snoop around on Facebook or other websites." They both mean investigate in an informal way which others don't feel comfortable with. Ozzie is right that "snoop" is more sneaky. People who "pry" may just be very curious e.g. family members, but people who "snoop" have a more serious intention and probably their actions and motives are less obvious e.g. when the police suspect a crime and start investigating.

They both mean the same thing but snoop sounds a bit more sneaky.