Tesla and SpaceX are both iterative technology. They both use existing technology and iterate improvements on it or apply it to new fields. The electric car was already proven feasible by GM and other companies or products like golf carts. It was more of a problem of the existing players being forced to build an electric car than keep doing what they've been doing to generate profits.
SpaceX still uses rockets. The new tech in SpaceX is changing the rocket design between engines so it is manufacturable in larger quantities and utilizing faster computers to create reusable rocket stages that can land with their own power back on Earth. You could say that SpaceX is leveraging computer science artificial intelligence research, the general improvement in computing (cost and speed), and sensors. For example there are many videos of software controlled quadcopters performing various aerobatic stunts by analyzing and adjusting thrust in realtime based on sensor information.
One could say there is nothing new in feedback control for vertical flight. It has even been coupled with GPS for precision motion and landing in rockets already many years ago by Armadillo Aerospace and others.
All this could have been done in the seventies, bar the GPS part, which would have required some more costly alternatives.
But even the V-2 had gyros on a free rotating platform that was connected to the thrust vectoring vanes that kept the rocket pointed to where the flight program required. The sensors weren't so good and you probably could not have throttled the V-2 to hover accurately, but maybe with radio guidance (that they actually used with some of the flights) it could have worked. Mechanical PID controllers date to late 1800s already (warship steering) so it was a totally straightforward thing to do, and was done by Goddard already. Nobody cared but the Germans...
SpaceX still uses rockets. The new tech in SpaceX is changing the rocket design between engines so it is manufacturable in larger quantities and utilizing faster computers to create reusable rocket stages that can land with their own power back on Earth. You could say that SpaceX is leveraging computer science artificial intelligence research, the general improvement in computing (cost and speed), and sensors. For example there are many videos of software controlled quadcopters performing various aerobatic stunts by analyzing and adjusting thrust in realtime based on sensor information.