NASA is still going to use the overpriced Space Launch System rocket to launch four astronauts aboard the Orion spacecraft for their multi-day journey to lunar orbit. There, two crew members will transfer to the SpaceX human landing system (HLS) for the final leg of their journey to the surface of the Moon. After approximately a week exploring the surface, they will board the lander for their short trip back to orbit where they will return to Orion and their colleagues before heading back to Earth.
NASA is still not fully shifting fully to SpaceX, yet. The first Artemis missions will still use an SLS and Orion to take four astronauts to lunar orbit. They will then transfer two over to the SpaceX lunar lander. SpaceX will refuel in low earth orbit (6 launches to get fully fueled). But this could be NASA pivoting to Starship and Super Heavy after the first lunar mission or two lunar missions. SpaceX Starship is bigger than a fully assembled Lunar Gateway.