Usually the differences are smallish. The difference between Nuisance and Minimal tends to matter not much.The technical details (for Conquests) are at this page. I don't pretend to have fully analyzed the formula, but the order is, from worst to best:
Catastrophic < Rampant < Problematic < Nuisance < Minimal
Although the difference between Problematic and Nuisance is often described as being Minimal.
Catastrophic is anarchy. That is 100% corruption without a chance to lower it. So that is category of it own.
Problematic is monarchy and feudalism. That is the default level of corruption.
Rampant is despotism. You get a 50% increase in distance corruption. Together with +25% distance corruption when not being connected to the capital this can get up to +87,5%. Distance corruption matters early one while later in the game courthouses and police stations each cut distance corruption in half.
Nuisance is republic and fascism. You get slightly lower rank corruption. You will hardly notice the difference to Problematic.
Minimal is democracy. In addition to the slightly lower rank corruption you get a 25% discount on distance corruption. In 4000 BC democracy would be quite powerful, but by th time you actually can becone a democracy a republic already has courthouses and it soon can have police stations, thus it is not worth the hassle of anarchy.
Communal corruption is better than minimal in the long run. It is a catagory of it own. If you exclude this special setting, then the remaining settings are already in the right order. Higher up in the editor means less corruption.