Potentially dumb ? re: travel

LSU628

I frequently see people posting that if the flight isn't full, they ask if they can bring their carseat onboard instead of gate checking it. If you are bringing your seat onboard, is your child sitting in the seat or they just stick it in an empty seat? We bought a seat for DD and will be bringing her carseat onboard, but to save some $ DS is flying as a lap child and we will be gate checking his seat.