Why do missiles have fins, while modern space rockets don’t?
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Fins are worthless in space because there is no air they can work on. Their effectiveness decrease when pressure drop at high altitude. The result is you need to have a rocket engine you can turn a bit to control the rocket, this is a gimbaled rocket engine.
The rocket had fins because it was a simple way to add extra stability close to the ground where the engine gimbal was not enough. But as technology improved the gimbaled engine was enough and the fins were removed because they result in drag and extra weight.
A gimbaled rocket engine is quite complete, so it adds weight and cost. If you only fly in the dense lower part of the atmosphere using fins is the cheap and light option so that is what missiles are used.
So space rockets add an engine gimbal system because they need a higher up and can skip the fins. Missiles that are quite close to the ground all the time so gimbaled engines are not required and fins are enough.
So both use the control methods most appropriate for the environment they operate in.
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