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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.