That's true. I think the taxonomy I'd really endorse is that the dichotomy is between free software and proprietary software, and within each there are a range of restrictions/guarantees (depending on your PoV: user or developer) that licenses might have.
The broad distinction we care about within free software is copyleft vs. permissive, and one important one in proprietary software is source-available vs. closed-source.
Then besides all of that there are the non-licensing realities of how development is actually carried out, whether it is collaborative with outsiders, and with which outsiders...
The terms get harder because open/closed suggests straightforward opposites that partition all the options. But I'd characterize licenses like BSL and the Fair Source License as 'generous proprietary licenses with public source availability', but not open-source.
I have a feeling that the term 'open-source' is more likely to erode than 'free software', in the coming decades. We'll see, I guess.