Yes - all Elon’s spaceX company but different launch systems for different purposes.
The space-x “starship” is the one which auto destructed - it’s the prototype vehicle to carry people and cargo to orbit, the moon, mars.
It was a successful test in that it got further than the previous ones. Nothing to do with starlink satellites.
space-x “falcon” are the ones that launch the starlink satellites.
to infinity and beyond !