The big rockets of the past were in very large part designed by NASA. The contractors did have a lot of input, but NASA drew up the detailed specifications and had the final say on every aspect of the design and engineering. Different components often had different manufacturers. For example each of the three stages of the Saturn 5 had a different manufacturer and all three were designed by NASA. The first stage was built by Boeing, but the F1 engines on it were made by Rocketdyne, all to NASA specs.

In contrast every aspect of the Falcon rocket and Dragon capsule design was determined by SpaceX. NASA set the overall goals and safety criteria, but you can see from the differences between the Starliner and Dragon designs how much scope the manufacturers had. It really is a completely different paradigm.