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A finer distinction would be "closed-source operating system".

There is nothing wrong selling a Linux-based OS/distribution.

No; and No.

Anything that is not licensed as "Free Software" or "Open-Source software" is "Commercial Operating System".

How does Red Hat Enterprise Linux fit into that classification? It's both commercial and open source.

That is not "Linux".

Linux can be commercial, look at RHEL, SuSE, Ubuntu. The moniker you're looking for is proprietary.

They're far more than Linux, in the sense that a product using Sqlite isn't "Sqlite".

Commercial has to make money somehow, directly or indirectly. Plenty of software has been released gratis over the years under proprietary licenses.

Replace commercial with non open source.