It’s the same thing in all cases: the meaning is in general “open to the general public”, often by opposition to what came before or what was the norm at the ti

It’s the same thing in all cases: the meaning is in general “open to the general public”, often by opposition to what came before or what was the norm at the time (private schools, private salons, and unlisted companies respectively; in all cases you needed to get invited or accepted somehow and entry was restricted). The issue is that language drifted and now “public” generally means “owned by the public” rather than merely “open to the public”.