Not necessarily true - that right to modify/redistribute depends on the exact license being applied.

If you don't have the right to modify and redistribute it (and to do so commercially) then it does not meet the definitions of free software or open source.

For example, the Open Watcom Public License claims to be an “open source” license, but it actually doesn’t allow making modifications.

The Sybase Open Watcom Public License does allow making modifications, and distributing modified versions. The reason why the FSF has not approved it is that it requires you to publish source code even if you only wanted to run your modified version yourself and didn't actually want to distribute anything to anyone. (The Watcom license is one of the few licenses which is approved by OSI but not FSF. You can see the other licenses which are approved by one but not the other by sorting this table.)

The FSF's own AGPL license is somewhat similar, but it only imposes the requirement if you run the software for someone else over a network. (Neither of these requirements are likely to be enforceable by copyright law, as I explained in my comment about the AGPL in the thread which this thread is about...)

This is also why we specifically have the terms “free software” or “FOSS” which imply they you are indeed allowed to modify and redistribute.

I would recommend reading this: https://www.gnu.org/philosophy/open-source-misses-the-point.en.html

I would recommend that you re-read that, because it actually explains that the two terms refer to essentially the same category of software licenses (while it advocates for using the term free software to emphasize the philosophical aspects of those licenses).