Finding minimal number of del/insert/change to transform string X(len=m) to string Y(len=n)

Question

I’ve read and pretty much understood the algorithm to solve this problem using only insert/delete actions, which completes the task in O(n * m)

I was thinking; if we were also able to change(replace) a character in the process, how would that affect/change the algorithm?

Would it matter in any sort of way, by running time / space requirements?

Thanks!