Consider this: a) literally zero government intervention. b) some government intervention, to keep the market competitive, as described above. c) total government control.

What do you, jlcoff, call a)? If I understood you correctly, it's "free market". What would you call b) and c) then?

There is no doubt that a) is strictly incompatible with any government regulation or intervention. Label those two concepts however you want, but I don't think anyone argumented against that.

A lot of people seem to use "Free Market" for b) instead of a) and that is confusing.

I agree with Diesel555's idea of calling b) a "competitive market" as it avoids a labeling confusion between a) and b).

b) and c) are either socialism or cronyism, or a variant of fascism (which is in its core a non-USSR controlled / nationalistic socialism).

Market is regulated by its very definition.

If it was completely unregulated, the person with the biggest gun would just take everything he wants.

It was always abut where to draw the line.