What is SpaceX doing that the Apollo project (or the Soviets, for that matter) wasn't doing 50 years ago. Re-usable booster stages is all I can really think of.
Beyond the cost aspect that other commenters have referred to, they're evolving tech. They're the first ones to have a working full-flow staged combustion cycle rocket engine (the Raptor, currently used in the Starship prototypes), something the Soviets tried before and failed. Their Dragon capsule was also a gigantic technological leap relative to the admittedly tried-and-true Soyuz, and it also looks far more comfortable for astronauts than the Soyuz does.
SpaceX is also doing right now what Apollo and the Soviets are not doing right now. That's very important, because they are using modern materials and manufacturing techniques and developing new concepts. If SpaceX (and soon their competitors, hopefully) manage to keep themselves in business (and they might, because of the profit motive, which is enduring, rather than national pride, which comes and goes), there's a fair chance our species might bootstrap its way out of the ancestral gravity well this time around.
Profit has not been the goal. If profit is the goal, one'd start another eyeball catching internet application. As the joke goes, the way to make a small fortune in space, is to start with a big fortune. SpaceX is the exception, not the norm. It worked only because of the unwavering, perhaps maniacal drive of one man. The man being hated on all over the place here that shall not be named.
I'd suspect the space industry will slow down drastically again if somehow that man stops putting space as a priority (or at least one of his priorities). Currently I don't think there's any one or company that is able to push the envelope AND still turn an operational profit at the same time. Even Starship program is not. Making it work is the exception, not some inevitable norm as others are making it as. Aka - "just because of government money".
Space is a perfect example that this isn't true. It kept going up and up with NASA/Boeing. The Space Shuttle ended up costing, in total, $2.2 billion per launch! [1] The SLS, if it ever finishes, was expected to cost more than $2 billion per launch [2], and that's before we went into inflation land. Add the inflation and the fact that expected costs tend to be dwarfed by real costs, and it's easy to see it going for $3+ billion per launch.
By contrast a Falcon 9 costs $0.07 billion per launch. And the entire goal of the Starship is to send that cost down another order of magnitude. Without significant competition + price sensitive market, the only way costs come down is if you have an ideologically motivated player. And it's fortunate that we have exactly that with SpaceX.
The overwhelming majority of SpaceX's revenue has been government contracting. That is starting to diversify in the last 2-3 years with more truly private launches and with Starlink, but that's relatively new, and even so government is a very, very large share of revenue.
Many were. I'm not saying this is terrible-- these programs cost too much for private entities to bear all the risk, and most of the programs that SpaceX has gotten funding from have been well-run programs.
COTS paid for vehicle development for Falcon-9 and Dragon; CRS paid for flights. COTS was a pretty well-managed program with a lot of clear milestones for funding release.
The troubled Artemis program has paid for a whole lot of Starship development and demonstration. It's questionable how well Starship actually meets Artemis needs, so this is more troubling.
And, of course, the government has bought early flights with no guarantee of success, including just to fly masses/demosats. DARPA/NASA/ORS paid for the first 3 Falcon I failures.
OK granted. NASA and legacy aerospace contractors were milking a cash cow and never thought they would face a new competitor.
But I was more thinking of fundamental capabilites. We (USA and USSR) have had crewed low-orbit space stations since the 1970s and have been sending astronauts to and from them since then. We sent probes to Mars and Venus and other planets in the 1970s. The Voyagers were launched in 1977. The stuff we're capable of doing today has not really advanced.