Yes, one builds on top of the other. That's how it works ideally.

It is however easier to get workers to unite when there's no legal minimum to fall back on. Also, when the majority of workers are unionized, the legal minimum is irrelevant and only serves as a talking point against the actual negotiations.

Minimum wage makes sense in countries where unions can't get a foothold, but it's a double edged sword: It's keeping unions from establishing, because a lot of people will gladly leave their negotiations up to the politicians and not risking sticking their nose out.

Quite a lot of the things that people take for granted now started as union contracts. Paid holidays, working hours being less han 80h/week, maternity/paternity/family leave, sick leave/pay, paid breaks, paid pension etc.etc.

NONE of that happened due to political parties feeling a need to require employers to pay out more or secure the working class.. Never happened.

It might be elevated to law in some countries by now, but it always always started with unions demanding it and going to conflict over it.

Even when the conflicts failed, it made the premises for putting it into law. That is how working hours have decreased. Unions wanted it, didn't get it at first, but still got it second time around, when the notion hit the government workers, making it necessary to lift the idea into law to keep functioning.

Without unions, we'd still be shoveling coal into a furnace 80 hours a week, because that's what made financial sense for the business owners.