you can switch between shuttles and starships. Go to the ship selector, on the left bottom there says: current ship: starship or small craft. You can fly with your shuttle in sector space and do missions, but thats a bad idea 'cause shuttles are just to weak for normal missions.
You will switch automatically, when you use your starship, to your small craft if you do a mission which requires a small craft. So you dont need to run to the next stabase and switch by yourself.