Edit distance between two strings

If X denotes the length of string s1 and Y denotes the length of the string s2, then the edit distance between s1 and s2 is never more than
Min(X,Y) or Max(X,Y)?
Let, $s1=a$, $s2=bb$
The edit distance between $s1,s2$ is 3 if allowed only insertions and deletions; but it is 2 if allowed insertions, deletions and substitutions.