Amend vs Emend : difference and meaning

Both these words mean to change for the better but with a small difference. 
The words are Amend and Emend.

Amend with an 'a' means to change in a broad sense. A change in law, change in behavior

Ex - He promised to amend his rude behavior in the future. 

Emend with an 'e' means to fix mistake only in written text.

Ex - I've emended the draft to ensure all the names are written correctly. 

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