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A liquid propelled rocket engine carries liquid oxydizer with it to create the combustion that will produce thrust. A cyrogenic rocket engine carries frozen oxydizer along instead.

The liquid propellant can be turned on and off, which allows for more control over the rocket, a lot like a jet engine. The solid, frozen oxydizer will keep the combustion going until it runs out. This is more common, as it is less expensive to construct, since it has less parts.