There are two types of gate checked bags. Proper gate checked bags get the full sized label that all other checked bags get, and are fully in the system, and if nothing goes wrong gets spit out at your final destination on baggage claim, like normal checked luggage.
Valet Checked bags use pink/red tags and are supposed to be returned on the jetway. It is supposed to be impossible for these bags not to be returned planeside, and are not supposed to get intermingled with the normally checked baggage. In practice I've seen this not work out first hand, with the bag ending up in baggage claim. (I've seen others say the same thing happened to them too. I suspect some airports actually have baggage handling set up to check for these if they get "into the system", and forward them to baggage claim, as the safest option.)
Valet Checked bags use pink/red tags and are supposed to be returned on the jetway. It is supposed to be impossible for these bags not to be returned planeside, and are not supposed to get intermingled with the normally checked baggage. In practice I've seen this not work out first hand, with the bag ending up in baggage claim. (I've seen others say the same thing happened to them too. I suspect some airports actually have baggage handling set up to check for these if they get "into the system", and forward them to baggage claim, as the safest option.)