Both ‘amid’ and ‘amidst’ are prepositions and they mean the same thing, technically. A preposition is a word which describe the relationship of two things in a sentence.
‘amid/amidst’ mean ‘in the middle of’ or ‘surrounded by’.
The addition of ‘st’ was a product of Middle English which added few extra letters to words, known as excrescent suffix. An excrescent suffix adds only sound — it does not change the meaning of a word. Examples are among (amongst) and while (whilst).
However, while British English uses both ‘amid’ and ‘amidst’, American English prefers ‘amid’.
Also, ‘amidst’ is often used in literary structures.
Meanwhile, ‘amid/amidst’ should not be confused with ‘among’: the former is used with mass or uncountable nouns (He stood his ground amid the controversy) while the latter is used with countable nouns (He stood among his friends).
In summary, the use of ‘amid’ and ‘amidst’ solely depend on your preferred form of English (British or American) or just your choice.