Grammar - Can

I'm starting to translate the New McGuffey First Reader. I have
a question about the word can.

I understand the purpose of 'can' in the sentence "I can run."
ie. "I am able to run." Or in the sentence "I can see" would
mean "I am not blind" or perhaps "There is enough light
for me to see by" or something similar.

But what is the purpose of 'can' in the sentence "I can
see the cat"? How is that different than the sentence "I see
the cat"?

Thanks,
scott

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