Modify term and extend term are identical AFTER the fact.  You could not look at a loan that had been modified or extended and figure out which was done.  So...

 

Q: How are they different?


A: The term defined in the four fields below is counted from the original origination date on a modify term, and counted from the maturity date (i.e. added on to the old term) on an extend.

 

Renew term does the same as extend, and also allows the entry of a renewal date.

 

This is mostly a matter of personal preference.  There is no correct answer to the question: when is it appropriate.