Levenshtein Your Source

Python 2 + sequtils, 101 bytes

from sequtils import*;_='from sequtils import*;_=%r;print edit(_%%_,input())';print edit(_%_,input())

Python 2, 278 258 bytes

t=input();s,f='t=input();s,f=%r,lambda m,n:m or n if m*n<1else-~min(f(m-1,n),f(m,n-1),f(m-1,n-1)-((s%%s)[m-1]==t[n-1]));print f(len(s%%s),len(t))',lambda m,n:m or n if m*n<1else-~min(f(m-1,n),f(m,n-1),f(m-1,n-1)-((s%s)[m-1]==t[n-1]));print f(len(s%s),len(t))

Try it online!

This is just the usual quine in Python, mixed with the Levenshtein algorithm from this answer. Note that it gets quite extremely (thanks to Mr. Xcoder :P) slow.