By-Election is conducted to fill a vacancy of a position ( eg. Ward member etc.) in a constituency.This may be due to the death or resignation of that particular person.  

Mid term election means electing the person in the middle of a term, when in an election, only some seats are up for grabs, to complete the term/ tenure of another member to avoid overcrowding. So, when the representative's term/tenure is over, he will be removed and a mid term election conducted to fill his seat. Pls mark as brainliest if this helped!