Oh dear… this may be a little difficult for you, but I’ll try…
Spacex uses a cooler grade of LOX, which is more dense than the LOX used by other launch vehicles. This increased density is around 0.75% to 1% greater than the density of “standard” LOX, meaning that there’s just that little bit more LOX than other rockets use. HOWEVER… it is more volatile, and has some “odd” physical properties (go look it all up - that’s one of the advantages of the internet). It’s partly the reason their rocket exploded on the launchpad last September (along with the configuration of the Helium pressure system). ULA (United Launch Alliance), ESA, the Chinese and the Russians will not use this supercooled LOX. Firstly, their engines and systems are not designed to handle the stuff, and they also consider it to be too “volatile”, so never bothered to design systems to accommodate it. Also, where governments fund programmes, there’s not a big incentive for economic resusability - they just use the taxpayers money and expend the entire vehicle.
The dynamics of power-to-weight and acceleration (via Newtonian Laws), as well as the Delta-v (go look that up too), plus this fractional “surplus” in LOX, allows Spacex to get the first stage to about 6000kmh, separate it, then come back down to earth. It’s extremely fine tolerances and the timing of ignitions, thrust volumes and EC’s (engine cutoff) are critical…
BUT… get it right, and it all comes together.
As I suggested, spend your next vacation in Florida and time it to coincide with a Spacex launch. If you see any “fake” stuff going on, I’d be pleased to hear about it.