Yes, the way they do this is weird. You're right that that is what percentile means. Although the two sections use the same scoring range (6 to 51), they do not use the same scoring
scale—ie, the same score levels don't mean the same thing on the two sections. So that is why you're seeing such a difference in the percentiles. The Verbal scoring scale hits 99th percentile at a score of 45, while the quant scoring scale tops out at 97th percentile for a score of 51.
Why do they do it this way? I don't know.
But, really, ignore the percentiles. Pay attention to the scores themselves.
The schools are looking for something different for Q and V. The top-10 (most competitive) schools generally think that a 36+ on verbal demonstrates competency (ie, you have the necessary competence to succeed in this area / with this skills). The equivalent Q figure is 45+. (Note: this does not means that you absolutely have to hit those scores in order to get in—but, if you fall below those scores, the schools might have some concerns and need to be reassured in other ways that your skills, especially on the quant side, are good enough for you to be able to succeed in their program.)
So if you are going for a top-10 school, you've got some work to do still to demonstrate competency on quant. Also, note one more thing if you are going for that kind of school: If you hit the "minimum" (V36, Q45), then your overall score will only be in the 660 range—so you will likely still be too low as far as the overall score is concerned (these schools have 700-730 averages, typically). So you do need to lift beyond the minimum in at least one of the sections—and that's usually easier to do in your stronger area.
That means that you also still have work to do on the verbal side (if you want that 700+ kind of score) to help lift your overall score. If you can hit V40 (91st percentile), then Q45 should get you to ~700.