It is not a denomination, it is a rite, a way of offering Holy Mass which has developed organically over hundreds or thousands of years. The action is the same, the prayers and their order differ somewhat. They are all in communion with Rome, and the Head of the Church is Jesus.
Don’t mind Gamecock, he’s just anxious for the Presbyterian Ordinariate. Not so much for the liturgy, but for the ability to hurl anathemas like an imperious medieval Pontiff.
;)