Bill Gates made the money and then spent it socially on vaccine research, reducing disease, improving education, etc.
Elon Musk's efforts are more directly social-entrepreneurial. He's helping to move the entire world away from gas powered vehicles (Tesla/Solar City), reducing urban congestion and improving rural life (SpaceX/Starlink), and trying to back up civilization on other planetary bodies (SpaceX).
I think the idea of "social entrepreneurship" is plagued by the problem of "serving two masters" when you really need focus to be successful.
Elon Musk clearly is clearly doing social entrepreneurship, but in practice that just means running successful (and relatively traditional) capitalist enterprises. Gates was even more conventional with his path. Both are doing a lot more good than most people who call themselves social entrepreneurs.