Edited question for posterity: The reason my resulting hash values were the same is that the I'm computing checksums of two .iso files which contain "empty strings."
I attempted to verify two different ISO files and didn't notice they had not completed downloading. Both files generated the same checksum, sha256sum: e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855 This the same checksum you would get for any empty string.
I had amended my original question to ask "What thing am testing to get the results I got?" The answer is, "an empty string."
I'm editing this because my original question and subsequent edits left a confusing question. It's answered.
Do the files really differ? Use this command to know:
If there are no differences, you should check their hash values from where you downloaded those files. They exist with a guide on the Linux Mint's site.