The difference between these is simple, and has to do with the intended target user.
Max/Min Temperature is computed from midnight to midnight (local time). This is most useful for data analytics, model training, and research. It is the method that aligns with what most daily climatological reporting stations report for their max/min temps.
High Temperature or the "Daytime High" is computed from 7AM to 7PM (daytime high) local time. Conversely, Low Temperature "The Nighttime Low" is computed from 7PM - 7AM the following morning (Local time). This is most useful when displaying data to the general public, and aligns with what News Stations typically show on their broadcasts. As it aligns with a typical work day.
For example, a person getting up at 7AM to get ready for work is likely more concerned about what the temperature will be when they go outside - not what the temperature was at the midnight before.