Johnnyloans Miracast, I think is from Microsoft and was/is extensively used for wireless displays in Windows, and widely adopted by Samsung in their OneUI also to be used in Samsung's desktop environment called DeX. Miracast doesn't require any internet connection to be used (p2p).
Chromecast is purely from Google, from what I recall it must use Internet and Google services to work reliable and thus I didn't use it. There was a thing called Guest mode on Chromecast, but I couldn't get it working having internet disabled.