Fastest way of finding differences between two files in unix?

I want to find the difference between two files and then put only the differences in a third file. I saw different approaches using awk, diff and comm. Are there any more ?

eg.Compare two files line by line and generate the difference in another file

eg.Copy differences between two files in unix

I need to know which is the fastest way of finding all the differences and listing them in a file for each of the cases below -

Case 1 - file2 = file1 + extra text appended.
Case 2 - file2 and file1 are different.