I try to use following definitions (of course, both are fuzzy and apply only to some extent in real world):

Free market: A system where the goods are distributed based on prices set through the market mechanism. In particular, anybody can produce and buy anything.

Capitalism: A system where there is a private ownership of capital and human labor is being sold/bought for a price.

So yeah, in theory, you can have free market without capitalism (for example everybody works for a worker cooperative), and capitalism (almost) without free market (there are distinct capitalists and worker classes, and market is heavily regulated or subsidized from the state).

Non-free market capitalism or heavily restrained free market capitalism is basically the programme of the far-right these days in a lot of countries. On the other side, you have Market Socialists (https://en.wikipedia.org/wiki/Market_socialism).

Free markets do require capitalism, but capitalism (as defined by using monetary capital as the primary resource) can unfortunately also operate in various less than free modes.