If you are not checking bags you can check in online for your other flight so you do not have to leave airside. Though you may have to leave airside if your departure gate is in another terminal and there is no airside connection.

If you are checking baggage most likely you must go to the check in counter again to drop it off for the new flight.

In the past I've heard checked bags get transferred to your other flight even though it is a different company/ticket, but personally I've never experienced that.

If you miss the flight due to the other one delaying you may lose your ticket. I have done this a lot I just make sure to give several hours between both flights.