When do I say something is difficult to do or hard to do
Or difficult to understand or hard to understand
Thus, when do I use difficult and when do I use hard?
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Both terms are synonyms, they mean the same.
According to Cambridge dictionary
hard adjective (DIFFICULT)
difficult to understand, do, experience, or deal with
not easy or simple; hard to do or to understand
EDITED: Take a look below to J.R's comment and to the linked entry of the dictionary. There are additional meanings of hard not shared by difficult.
hard adjective (SOLID)
hard adjective (SEVERE)
hard adjective (ALCOHOL) - A hard drink contains a high level of alcohol
hard adjective (WATER) - Hard water contains a high level of minerals
hard adjective (WEATHER) - Used to describe a time when there is bad weather