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.