Yes, a SSD is a hard drive made from flash memory, which is why it's so fast.
You will need to install Windows on it. You've got a few options here. You can download a Windows disc here
, then do a clean install. Thinkpad's Rescue and Recovery can do a format to the factory state then restore the drive to however it is now if you do a Rescue and Recovery back up. Your other option would some sort of cloning of the hard drive. Something like the True Image can clone the drive and put it back like it was before, but the thing you have to be concerned about with those two options is whether they will set partition alignment correctly. I don't have an answer for that, but to get the best performance, you'll want to have it aligned correctly. Perhaps someone more knowledgeable than I can post. If you do the clean install Windows will align the partition properly, but that's a lot more work.
Unlike the X220, the X200 doesn't have any mSATA options. You might want to consider the Seagate Momentus XT. It's a platter based drive with a 4GB flash drive attached. It gives near SSD performance while offering up to 500GB of storage capacity.