I have been doing some research and realized that I missed the fact that in ISO 9126 and ISO 25010, all characteristics are quality characteristics and represent (according to various papers) just non-functional ones. It surprised me as I thought "Functionality" is clearly functional but now I can see that they probably mean "evaluation of functionality from the non-functional view, i.e. how is the system doing these things".
Then I found an interesting thing in an ISTQB book. They talk about functional tests and reference ISO 9126 Functionality. But in the non-functional testing section, they enumerate non-functional requirements according to this ISO and do state Functionality, referencing the section in Functional testing page!
ISO 25010 is said to present 8 non-functional categories, including Functional suitability. That does sound like a non functional one but again it is said it is just renamed Functionality from ISO 9126. And yet there are books saying that "Functional suitability" from ISO 25010 is functional and should be tested functionally (well, it does make sense more than saying it is non-functional)...
Most of the QA books typically lists ISO 9126 Functionality under Functional testing so I cannot understand how this can be listed as non-functional...
Similarly, I found for the ISO 9126 sources claiming that its Functionality is quality requirement, therefore non-functional requirement, while the other sources state that non-functional are those except for this one.
Does anyone know this ISO standard well enough to explain the problem?