Finding common structure in strings
What you're describing seems to be isomorphisms between strings. (Note that there happens to be a more complicated notion that is also called 'string isomorphism', but that isn't what we're talking about here.)

You can 'describe the structure' of these strings as follows: replace each character with the number of different characters excluding itself before it in the original string. If you do this for the three strings you mentioned, you get the string '00100' in all three cases. 

This also gives an algorithm to test whether two strings are isomorphic: apply the above transformation on both strings and test whether the results are equal.