@jennythelib - Synthetic rubber has the properties of rubber, mostly its elasticity. It can substitute for rubber, whereas ordinary plastic just can't. It comes from the same material as plastic, but is processed differently. And that's about all I know - maybe someone with a chemistry background can fill us in a little better!
Now that plastic is everywhere, it's hard to image that rubber was once of critical importance. European's need for rubber was a big factor in the colonization of Africa and the resulting disruption (which continues today, of course). Believe it or not, I remember learning about that in an English class! (We were discussing colonialism.)