The attendant will put a luggage sticker on listing the airport destination, just like they do luggage. They put the luggage on the belt to the back, but you must carry your car seats to the oversized luggage are (usually close to the check in.) They will take the car seats from you there. I keep my stroller through secuirty an dthen gate check it. Gate check means you get a tag from the SW kiosk near your gate. You push the stroller all the way to the plane. At the plane door, fold up the stroller and leave it there. A luggage handler will carry it down the steps and place it beneath the plane. When you arrive at MCO, the stroller will be waiting for you at the plane door as they carry the wheelchairs and strollers to the plane door right away.
In some airports, checked car seats do not come out on the same belt as the luggage at baggage claim. Some they come out on an oversized area. At MCO and SFB, my car seats have always come out with the regular belt, though.
And, no, strollers and car seats and boosters do NOT count against your limit on any airline.