I think you are mistaken; neither is a subset of the other. At the very least, there are licences which are recognised as open source by the OSI, but not as free by the FSF, and vice versa [1]. I think it’s more appropriate to say they are two fundamentally separate definitions with a massive overlap.

[1] https://spdx.org/licenses/

Thank you for the information! I was not aware of the FSF's definition.

> Not all free software is open sourc

Depends on which "free software" definition you're referring to.

The FSF definition of "free software" requires it to be open source.

I have clarified which definition I used.

> Edit: I was not aware of the FSF's definition. I was using a definition of free software being software that you can use without having to pay for it.

That’s called freeware. Also, open-source software can be paid (with the caveat that if someone buys it, you must allow them to redistribute it for free).

You have recited a successful incantation to summon the Stallman acolytes.

To add an additional suggestion, gratis can also be used to refer to free as in free beer. Comes from a latin root and is common in spanish speaking countries to refer only to free of charge, and not as in freedom.