Before I proceed, I would like to first acknowledge that there are similar posts to my question, but I didn't seem to understand fully. So allow me to elaborate on my inquiry.
If I view the term "isomorphic" as the mathematical translation of:
"two structures not only look alike, but behave exactly the same way", or "facts are preserved in between two structures".
Then how do I view natural isomorphism, as the term currently feels 'artificial' to me. All I know is how natural isomorphism arises from natural transformation, which a morphism of Functors.
Thanks and cheers !