This is the Space Launch System (SLS):
You can say that in a way it is a child to the Space shuttle, or the space transportation system (STS)
because the SLS rocket uses alot of the same parts as the space shuttle.
So NASA isn't using any Space X ships (like the Starship) to get back to the Moon, here is the Artemis 1 mission patch:
(btw, Artemis is the name of the program that focuses on getting back to the Moon. The Artemis program is named after the twin sister of Apollo.)
The capsule that will be used is the Orion space capsule
The SLS and Orion might also be used for future Mars missions.