IMO both of these ended up being poor names.
"Open source" can be co-opted to mean any project with public source code even if it's not open contribution (think SQLite, and many of the projects effectively run by major tech corporations).
"Free software" falls victim to the eternal mixup with freeware, requiring the endless repetition of the "beer vs. speech" analogy.
I personally think "Libre software" is the term that best encapsulates the intended meaning while being unambiguous and not vulnerable to misinterpretation.