Your sources contradict your premise. The core tenants of the two are the same; many of those who prefer the term "Free Software" do so because the term "Open Source" implies that providing the source code is all that's necessary, but at least "Open Source" as used by the OSD is synonymous.

OSI #5-10 are kind of a spelled out form of Freedom 0

OSI #2 maps pretty much directly onto Freedom 1 (The title of OSI #2 just says source code, but the body text specifies more)

OSI #1 is Freedom 2

OSI #3 maps to Freedom 3, with #4 being a clarification of what is allowed.