They're pretty much the same thing. There are options that involve pulling the battery while the device is on, but that's not, I believe, what's needed here. A factory reset puts the device back into it's out-of-the box state, though with whatever version of the firmware it was running (ie including updates) at the time. It clears app and system caches, which I suspect are the problem here. You'll find the option in the Settings menu, often under Security or Storage.
I suggested clearing data on the Contacts app as that might solve the issue if it's confined to that area. However, if you've done a firmware update, bits of the old code can hang around and confuse the system, causing all sorts of odd behaviour. A factory reset clears them out.
The process will delete all your data, so make sure your contacts and calendar are fully syncd before you start, and that you've backed up things like music, photos and documents. I prefer the file-by-file method, with the phone connected to a pc as external storage. It's also advisable to remove the external sd card, if you have one, as resetting often erases that, too.
