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.
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.
> 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).
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.