The two verbs have very similar meanings.
look at something quickly without being seen (secretly)
- Janet told me not to look in her drawer, but I couldn’t resist peeking in.
- I was so nervous before my first concert and it just got worse when I peeked at the audience from behind the curtain.
look at something quickly and secretly through a hole/opening
- What are you doing peeping through that keyhole?
- I got so scared the other night. There was someone peeping through the little window over my bathtub.