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
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