A website called whatgamesare.com is a good place if you just want a list relevant terminology. At the end of the day it only matters when you can apply it.
I like the post by Ludus above. While I would say people have been studying games for as long as games have been around (thousands of years), academia has really only taken notice of it recently with the rise of video games so nothing is in stone and probably won't be for a long time. Even a lot of the definitions given at whatgamesare.com I don't agree with completely.
The process of game design is more important than the terminology. Learn the process and the terminology will come along with it, molded to the way you see things.
I hope what I said makes sense. I've never really thought about understanding game design solely through accepted terminology. You have to play games, make games, and connect the dots.