Thanks for your questions –
Actually, Big is a adjective word: big; comparative adjective: bigger; superlative adjective: biggest
Word Origin
Middle English (in the sense ‘strong, mighty’): of unknown origin.
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on the other hand, LARGE is a adjective word:  Large adjective: large; comparative adjective: larger; superlative adjective: largest
Word Origin
Middle English (in the sense ‘liberal in giving, lavish, ample in quantity’): via Old French from Latin larga, feminine of largus ‘copious.’
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Large is used to convey size only, while big can be used to convey importance or power.
Here I have tried to clarify you –
A large man – means a man of above average size.
A big man – may mean a man of above average size, but may also mean an important or meaningful man, as in, “Big man on campus.”

When applied to non-physical object, large continues to mean size, even if the result is nonsensical.
A big idea – means an important or powerful idea.
A large idea – would mean an idea that has more size than a regular idea.

A big day vs. a large day – A big day is an important one, a large day would be one with more than 24 hours.

A big deal vs. a large deal – A large deal could mean one involving either large amounts of money or large companies, where a big deal could be small in size, but important in scope.

While both are Middle English words, the word large is derived from the Latin adjective largus (largi, largae, etc.) meaning abundant. The word big is of Germanic origin.

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