[ceejayoz]

They absolutely compete. SLS and Starship, for example.

[aerostable_slug]

Boeing builds SLS, not NASA. NASA is the paying customer.

[ceejayoz]

Boeing builds SLS to NASA's specs. They're a contractor; Boeing has no other use for the rocket.

Starship is a very different scenario; SpaceX fully intends for it to serve their own purposes as well.