The principal difference is the NASA involvement and its forms. For Mercury/Gemini/Apollo/Shuttle NASA designed, managed and ordered spacecrafts. For Crew Drago

The principal difference is the NASA involvement and its forms. For Mercury/Gemini/Apollo/Shuttle NASA designed, managed and ordered spacecrafts. For Crew Dragon, NASA buys launches - with a lot of say in how the spacecraft should be built and behaved, but still not on the level of project initiator, as it happened before. SpaceX is a bigger author of its manned spacecraft than any private company ever was.