I will use some of these terms in this book.
The "Open Source" label was created in February 1998 by a team of individuals who would subsequently create the organization Open Source Initiative that same month.
"Open Source" is a ten-point definition declaring that if those requirements are all fulfilled, a software component qualifies as Open Source. It should allow free redistribution, modification, derived works, not discriminate against any person or field of endeavor etc.
Proponents of Free Software often underscore that there is a difference between Free Software and Open Source, but in practice, looking at the requirements and the licenses involved, those differences are more distinct in the communities and how they operate rather in how they are defined in text.
Open Source was an effort to create a term that emphasizes the open aspect, as a more commercially friendly phrase and concept than how many people perceived Free Software at the time.
The Free Software movement is oriented around the Free Software Foundation that was created in 1985. Free Software has their four freedoms that decide if a software qualifies. The freedom to run it for any purpose, to study how it works and to change it, to redistribute it and to redistribute modified versions.
Note that there is no mentioning of price or commercial in there. Free is used here as in freedom, not as in price or cost.
Free and Open Source Software (FOSS) is a commonly used acronym meant to include software that qualifies as either Free Software or Open Source.
There are both longer and shorter versions of this being used:
Free, Libre and Open Source Software (FLOSS) is an attempt to emphasize the "libre" part as in freedom and not price.
Open Source Software (OSS) leaves out the "Free Software" part but generally it refers to the same group of software, maybe just not as technically correct.