The FSF and OSI both disagree with you.
The old BSD 4-clause is a FSF approved Free Software License. It is not an OSI-approved Open Source License (because of the advertising clause.) The newer 2- and 3-clause BSD licenses and the GPL are all both FSF Free Software and OSI Open Source licenses. What they do demonstrate is the distinction the FSF makes between copyleft Free Software licenses (which the GPL is), and non-copyleft Free Software licenses (which the BSD Licenses are)
But Free Software and Open Source are almost identical.