Comprehension usually used with of. Or about how something works: Understanding a concept means you get it.
PPT 9 A digression on the economic costs of war PowerPoint
Knowledge about a subject, situation, etc. He noted bond's apparent lack of. Both comprehension and understanding can be used to talk about someone's ability to understand something.
Understanding implies abilities and dispositions with respect to an object.
Understanding is a relation between the knower and an object of understanding. How to use understanding in a sentence. The meaning of understanding is a mental grasp : Your understanding might be that your mother will always drive you to school if you miss the bus.