A rocket uses an engine that creates thrust through the combustion of a liquid fuel and an oxidizer. What kind of rocket is this?

I believe this is a rocket engine. A rocket carries its own supply of oxygen aboard the vehicle. An example shown below is the liquid rocket engine. This class of rocket carries a liquid fuel and a liquid oxidizer in two separate tanks. The two liquids are pumped into a combustion chamber at some rate where they are mixed and burned.