The difference is fairly simple... A relay is everything a remote is, plus it can also host another router that extends the same network even farther, like in this picture:
So, if you have three or more routers, you can form a chain of three of them like in the picture. Otherwise you just use remote.
If you think of it as like links on a chain, the remotes are "ends" of the chain, but the relays are "in the middle."