A space station stays in space, but a shuttle carries people from one place to another. Just as on earth, my town has a train station that never moves and a shuttle bus that takes you to the station from the middle of town. Our train station is a little out of town. Either sentence is grammatically correct. It depends what you want to say.

space shuttles and space stations are both sent to outer space, but they are different contraptions.

The sentence is grammatically correct either way, so this is a question of fact, not language. I imagine that they send shuttles into space, and then construct the space stations on site (i.e. already in orbit). I'm an English teacher, not a rocket scientist, so take my answer with a grain of salt :)

Both are correct. They can send a station or they can send a shuttle.