Why do missiles have fins, while modern space rockets don’t?
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Lots of reasons. Here are a couple.
First, fins don’t work in space, so you’d need a different system, like steerable engines, in space. Since you need that anyway, adding fins would just be some extra weight, and it’s very expensive to add weight to a rocket that’s aiming for orbit. Missiles generally spend their whole flight time in the air, so fins work fine for them.
Second, missiles need to be able to turn fairly quickly, in order to hit their target. Fins work better for fast turns. Rockets really don’t need to turn that quickly, because they’re going to be flying much longer, and there’s time to make small corrections to get where they want.
SpaceX boosters use a kind of fins when they land, because they’d need legs to hold them upright anyway, so having those legs work as fins on the way down just makes sense. They don’t add much drag, because they’re folded during launch, and when they’re coming down, drag is a good thing, because it slows them down a bit.
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