In Czech we sometimes say: "Rozumím, ale nechápu." :-)
For example, in language, you can "understand=rozumět" every word that you're being told, but if the person is using idioms or terms that have a different meaning when used together compared to when you use each individually, you'll not "understand=chápat". The two are often interchangeable, but for "chápat" you get to the core of the problem and understand the logic how it works for example.
Yes and no... comprehend has no different meaning than understand. If someone said this though, a native speaker would fathom the meaning intended but it would have the same meaning as with the words reverse. So 'I comprehend, but I don't understand.' means the same as 'I understand but I don't comprehend'.
Again, it's not the comprehend means anything different than understand, it's just that one would hopefully grasp the meaning through a logical deduction.
I will speak to the English a second, knowing the Czech may be different:
I understand the words but don't know what you mean by them. = I know the words well but don't understand what you mean by them.
Know, understand, comprehend are mostly equal and the context or additional detail added clarifies.
One can also say, I know what you are saying but don't know what you mean. The choice in English is yours.
Rozumim means you understand the method of the communication. Chapu means that you understand the meaning of it.
So it's something like, if you have 1+1=... Understanding that this is a question asking you to solve what 1+1 is to rozumim.
Understanding the answer is 2 is to Chapu.
Not a perfect analogy but oh well.