Markets are usually about trading goods and services (buying and selling), and an enterprise is usually about generating goods and services. However, most people probably wouldn’t distinguish between the terms “free market” and “free enterprise,” because their understanding of economic and political terminology is too impoverished. They would conflate them fully with the ideology of laissez-faire capitalism. And that adds a whole other can of worms about what role ownership plays, indeed what ownership is, in the economy.
It’s like the terms right-wing, liberal, left-wing, and conservative. Few people actually know what they mean. These are all incredibly loaded terms that allow people to attribute to them whatever meaning they want, and avoid having a discussion.