I feel like these two tags are mostly synonymous.
Both are about understanding a sentence. I agree that "Parsing" is more of an analysis and micro-inspection of which part of the text while "Reading Comprehension" is more about the macro of the text.
However, at the end of the day when its about a language you can't really answer a reading comprehension question without explaining the parts of the sentence, that is unless you just correct the reading error without explaining why it was an error.
So while they may be separate in theory, in practice I don't think you can do reading comprehension without explaining how the text should be parsed.
What are your thoughts on the matter?