But they just don't happen to be doing the same thing. People claiming otherwise have to first prove that we are comparing the same thing.

This whole strand of “inteligence is just a compression” may be possible but it's just as likely (if not a massively more likely) that compression is just a small piece or even not at all how biological inteligence works.

In your analogy it's more like comparing modern calculator to a book. They might have same answers but calculator gets to them through completely different process. The process is the key part. I think more people would be excited by a calculator that only counts till 99 than a super massive book that has all the math results ever produced by the human kind.