What's the difference between polling and pulling?

They're two distinct words. To "poll" is to ask for an answer. To "pull" is to use force to move (actually or conceptually) something towards oneself (again, actually or conceptually).

One "polls" a server when software on a client periodically asks the server for something. One "pulls" data from a database towards client software.

Note that both words have various distinct uses even within the world of computing, but I can't think of any case where they're interchangeable in such a way as to leave meaning unchanged. Low-level device driver code may "poll" an interface to check whether it's ready for some operation, and there's no network traffic involved. In electronics, one "pulls" a signal up or down.

Clients may both "poll" a server and "pull" data from a server, but note that when I use each verb I use different direct objects. It only makes sense to say "pull the server" when you're dragging it across the computer room floor.

Poll is like when Gallup does a poll of the American people. They are querying for specific information by asking a question.

Pull is like what you do to a rope. You want the rope (or a file, or some data) to be in your location, so you pull it towards you.

There is a possible slight difference.

Polling is attempting to request information at set intervals.

Pulling just refers to the fact that you are requesting data from somebody else rather than having them send it to you.

That being said, I've heard them used interchangeably.