Yeah, she definitely added some political fluff to the point. I think the broader point that she wasn't saying "individualism is great, sod everyone", which is often how its portrayed, still stands.

Yes they are. That's what she meant: society doesn't exist and families/individual people do. The distinction is that you can ask a family or a person to do something and decide if they did it or not. You can't ask "society" to do anything: what does that actually mean? Who does it? Everyone can just point the finger at everyone else.

Thatcher was making this argument because in the 1980s the [British] left was still very Marxist, so they tended to demand extremely expensive things and when challenged as to who will do/pay for that they'd answer with society. It was a form of rhetorical evasion because what they actually meant was "someone else but not me". Thatcher was railing against that tactic by pointing out that there isn't some specific entity with a big wad of cash you can go to called Society and ask them to do something. Society is your neighbours, your friends, your coworkers, your family, it's you and everyone around you. So if you say society should pay, what you actually mean is the people around you should pay but not yourself, without being willing to say so clearly.

Arguably the post-Marx neo-left actually did listen to her and stopped talking like that. You didn't hear people like Tony Blair claim that "society" would pay for their latest ideas. But the old left were never willing to give up the stupid linguistic game playing and reacted by fully stripping her words of context, to try and make it sound like she rejected the idea of bonds between people. Which is not only not what she said, but the conservatism she stood for was all about the primacy of friends/family/workplace/church/social clubs etc, vs the alternative Tony Benn style worldview in which the primary organizing unit of people was either the state or the unions.