It is a rocket. The biggest difference with the Falcon 9 first stage is that this one is about 6 times as big (diameter of 9m vs 3.7m), and that catching it with the tower requires a much higher precision in landing location. The drone ships that Falcon 9 lands on are about 90 x 50 meter. To catch it with the tower, they need to be accurate to within a few meters.

The big advantage of catching it with the tower is that it'll (eventually) allow them to put another Starship on top, refuel and launch again within hours, as opposed to the weeks it currently takes for Falcon 9.