They appear to me to mean almost if not exactly the same thing, but I am not sure. Are there differences in meaning between them?
They are related, but they don't mean the same, not by a long shot.
"Pending" means something that one is waiting for. "Patent pending"; a patent for this has been applied for, but it has not yet been granted. Or "pending confirmation of these changes to the contract, we will sign it".
Whereas "impending" means something that is about to happen soon(-ish). Hmm, I can only think of "impending doom". ;-)
You wouldn't use one for the other. "Pending doom"? No, certainly not synonyms.
All this from memory, I'm too much of a lazy bastard to look it up. ;-)
Have a look at grammarist.com They have a nice article explaining the difference between pending and impending. They also provide examples of usages.