Are security levels a gradation of something or just incomparable classes for easy management?

Using prisoner classes purely as a management category has a few pitfalls.

1. It makes sense to keep the separation of prisoners into the "min", "medium" and "max" classes, because prisoners which arrive with these designations tend to behave differently. The lower security prisoners will usually be rather easy to manage while the max security prisoners tend to be a lot more aggressive and are more likely to have some of the more annoying character traits like "Stoic", "Instigator", "Skilled Fighter", etc.. If you are smart, you take that into account when you design your prison. The min security areas usually need fewer guards. You also do not necessarily need to fulfill all the needs of low security prisoners because they are less likely to riot. Yes, it seems a bit counter-intuitive to treat min-sec prisoners worse than max-sec prisoners, but that's prison-life.
2. When a prisoner commits a murder while in your prison, their security rank designation automatically increases by one. This can be annoying when you use categories for a different purpose.

The "Protective Custody" and "Supermax" categories are mechanically identical. It is recommended that you use "Protective Custody" for inmates which are likely to become victims of other prisoners ("Ex Law Enforcement", "Snitch"...) while you use "Supermax" for those who are especially likely to commit violent acts. But if you decide to treat these two the other way around, nothing bad should happen. You might even consider to put both of these in the same category. After all, supermax prisoners also need to be prevented from killing each other, and just because an inmate is endangered does not mean they aren't dangerous themselves. So you might even treat them exactly the same (spend as much time as feasible in personal cells and always schedule multiple guards to accompany them when they must leave them).

Guards will not change the way they behave based off what security a prisoner is, however you may choose to have more guards/armed guards present with the higher security prisoners as they're more troublesome (note that things such as gangs - and certain attributes such as "cop killer" will effect the way guards will interact with prisoners, and these are more common with Max sec prisoners.)

Also, you can do it the other way round if you prefer to - not entirely sure why you would, but you can yes. (note - don't get the two confused, you want to keep protective custody VERY far away from people you're putting into supermax xD)