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