These terms are often used as if they are interchangeable, but they are not. Source code can be open, and yet, its license might not grant the users necessary freedoms for the software to be classified as FOSS.
I do agree that "Open Source" is a flashier term and much more popular, yet, when we specifically talk about project licenses, I prefer to be specific.
If the license doesn't grant the users freedoms, it won't match the definition. A commonly used term for software that has its source code public but isn't FLOSS is "source available".
Let's just collapse on some specifics, then? Please correct any inaccuracies in the below:
Licenses promoted by FSF qualify as "Free/Libre software" - GPLv2, GPLv3, AGPL. These also qualify as "Open source" per OSI.
Licenses which qualify as "Open source" but not "Free": Apache, MIT, BSD-like.
See: https://www.gnu.org/licenses/license-list.html and https://opensource.org/licenses
The distinction came basically because of political reasons. The term "Free Software" is about user freedom; the term "Open Source" has been coined so you don't have to refer to scary freedoms when presenting practical aspects of FLOSS to businesses. That's more or less the whole reason why those are separate terms, and also why FSF doesn't like the latter one.
Common usage has matched the OSI definition for decades. Even Wikipedia acknowledges it [0]. There are always some people who are confused about the terms, sure, but those usually come simply from lack of exposure and experience around FLOSS communities. Trademarks have nothing to do with it; it's not OSI that owns the term, but the community that uses it and widely agrees with OSI's definition.
[0] https://en.wikipedia.org/wiki/Open-source_software#Definitio...
the obvious meaning for the expression “open source software” is “You can look at the source code.” This is a much weaker criterion than free software; it includes free software, but also some proprietary programs, including Xv, and Qt under its original license (before the QPL).
That obvious meaning for “open source” is not the meaning that its advocates intend. The result is that most people misunderstand what those advocates are advocating. Here is how writer Neal Stephenson defined “open source”:
Linux is “open source” software meaning, simply, that anyone can get copies of its source code files."
i wouldn't call Stephenson's confusion here a rare occurrence; "Source available" hasn't really caught on, but instead open source remains ambiguous