That was Adam smith's definition when he coined the term...

Whenever I hear people talk about free market it is usually not in the sense of economic freedom or free software. So you are correct. It generally refers to free as in free beer aka the government is supposed to subsidize the private sector and average citizens are supposed to pay for it. I'm not talking about socialists here, I'm talking about neoclassical economists and neoliberals in business and politics.

Almost nobody wants to pay for the pollution they cause via CO2 taxes. Meanwhile income taxes are considered efficient despite their dead weight loss. Everything is upside down on this planet when it comes to economics.