Here's my opinion, as a bit of an outsider. Mainly, I understand MAX to mean the largest value in a finite totally ordered set. I understand TOP to mean the 'best' member of a finite set.

For example, on a mountain each point has a HEIGHT. There will be a MAX HEIGHT. The point(s) on the mountain that is the highest is the SUMMIT. Or in other words the TOP of the mountain. Or another example, there are TOP 40 charts for music. https://www.officialcharts.com/

To summarize, use MAX for the largest value in a totally ordered set. Use TOP when you have a height (or similar) function applied to an unordered set. The highest temperature in 2021 will occur on the hottest day(s). One is a temperature, the other a date.

I'm an outsider, and I've not made an effort to gain special knowledge about the domain prior to posting this opinion. I hope it helps. Please ignore it if it does not.

Jonathan