Can you name some examples? According to the internet for most practical purposes the terms "open source" and "free software" refer to the same set of licenses [0]
It's hard to sell air, until you compress it and put it in a tank. And it's hard to sell sand, until you put it in a bag. So the air and sand is free, but then it varies: Open core, dual licenses, packed with proprietary software, license clause's, etc.
Why not just ask for a license fee? And why can't something be open source when it's not free as in free beer? So yes, what I mean is there are open source software that is not free as in libre, and there are open source software that are not free as in free beer. So why can't this software be called open source, when the source is... open? Open source comes with many advantages, not just that it's free as in free beer but also that you can fix issues yourself, and it makes it easier to create plugins, mods, etc.
> And why can't something be open source when it's not free as in free beer
There is nothing preventing you from charging a fee for Open Source or even for Free Software. You only need to distribute source code to users of your software. That means it does not need to be publicly available on a site like Github. You need to remember that users who receive the software and source code are still allowed to distribute your software for a fee or even free. This method of selling software is not common at all though, so I can't really name any successful projects doing it.
> So why can't this software be called open source, when the source is... open?
The reason you can't call software like that as Open Source is because Open Source has a clear definition as defined by the Open Source Initiative[1]. Free Software has a definition as well[2]. The Open Source definition is a more expanded and detailed version of the Free Software's Four Freedoms. If the license you use for your software does not allow the things as described by those definitions, you can't call it Open Source or Free Software.