Moving is simply the process of transferring one thread from a forum to another forum, where the location is more appropriate. If you see a thread in a wrong location, just report it. It's not an offense to post your threads in the wrong place, but it would save us a lot of trouble if everyone could look at all the forums and find the correct place to post his or her own thread.
Merging, on the other hand, is an action that moderators hardly do. Once in a blue moon, a situation where we need to put two threads together will arise. One example was the one where I merged the guides in the Gaming Discussion forum due to a plethora of stickied threads, but the problem is, you can't separate those threads. I do not think we'll need to merge any thread in the near future.
The most common action a moderator does is locking. I'm sure you know why. And that summarises the job of a mod. Locking, moving and warning. There's absolutely nothing else. :O