The creators of both terms agree. I asked them:
http://jordi.inversethought.com/blog/5-things-we-have-forgot...
And here:
http://jordi.inversethought.com/blog/5-things-we-have-forgot...
And here:
https://www.gnu.org/philosophy/open-source-misses-the-point....
And especially:
"The two terms describe almost the same category of software, but they stand for views based on fundamentally different values. Open source is a development methodology; free software is a social movement.... Most discussion of 'open source' pays no attention to right and wrong, only to popularity and success..."
And of course OSI officially wrote "We realized it was time to dump the confrontational attitude that has been associated with 'free software' in the past and sell the idea strictly on the same pragmatic, business-case grounds that motivated Netscape." (http://web.archive.org/web/19981206185148/http://www.opensou...)
In other words, "open source" was about depoliticizing "free software" to make it more commercially palatable. (And arguably, it worked.)
Kind of like machine learning instead of statistics.
1996:
https://groups.google.com/d/msg/no.linux/1UZo-3iv0tM/XPrPljd...
1995:
https://groups.google.com/d/msg/comp.graphics.raytracing/6oZ...
While it sounds pretty brain-dead to put "open" in front of anything, to the point that it seems like the most natural thing for it, most people did not use this term and there was very little widespread understanding of what "open source" meant. If it wasn't for OSI, we'd still be saying a bunch of disjointed things instead of being universally aware of something called "open source".
Every time I have this discussion, someone comes along and thinks, "wait a minute, there's no way that OSI coined that term", but yes, they did. This is probably a Mandela effect.