They all mostly run android with GMS. They do apply their own skin, and sometimes Manufactures try to market it as a seperate OS. For example "NothingOS" in the Nothing phones, which is just stock android with a fancy skin applied.
I'm not all that keen on Samsung myself, but the 'and shit' here is a stand-in for the other makers of android phones for the US market. I'm sure google would be happy to supply a list, but I can't be fucked to go find it.