sir /madam

To comprehend means to understand, often deeply and completely.
To perceive means "to see." I can see something and not understand it. Often perceive carries with it the meaning of being aware of, and beginning to understand something.
Just in terms of my own reaction to the terms, "perception" = "message received," and "comprehension" = "message understood."

I recognize two common senses of "perception." There's the scientific sense, which is neurological. I'm not sure at what point IN the processing of sensory information perception stops.

Then there's the personal side of it, as sometimes comes out in the courtroom. Two people observe the same phenomenon but their perceptions differ. So we often hear dumb questions like, "What is your perception of democracy?", which probably means something like, "What is your conception of democracy?", or "Everybody has a right to his own opinion." I think this is taking "perception" too far. However, I think it's correct to say that Joe perceives the dog as a threat, while Bill perceives the dog as a potentially pleasurable experience. It's still neurological, but on the involuntary level.

When we come to comparing our memories of sensory impressions from some event, I think it becomes argumentative as to how much of that is perception.

People might say, "What is your comprehension of democracy?" meaning "How do you understand it?" I think this is incorrect. When used this way it is equivalent to the popular usage of "perception." That is, "What is your conception of etc.?"

I think the act of comprehending is the act of successfully reproducing some concept or logical construction in your own mind - to grasp something. I think it's correct to ask, "Do you comprehend (understand) what I'm telling you?" (An affirmative reply would not necessarily be proof of success.)

"Do you comprehend the law of supply and demand?" "Do you understand it?" Of course there may be different levels/degrees of comprehending/understanding.
His level of comprehension is equivalent to that of a ten-year-old. He only partially understands the social significance of what he has done.
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To comprehend = to understand.
To perceive = to realize.

i.e I don't comprehend the situation (I don't understand the situation)
As I walked I perceived there was someone behind me. (As I walked I realized there was someone behind me)
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