I think you're mistaken. The top hexidecimal value is the key ID. That's what they're explaining at the top of the search results page with:
Type bits/keyID cr. time exp time key expir.
The second line with "Hash=" is the fingerprint of the public key calculated with MD5.
Fingerprints and hashes are functionally similar in that they are both produced by one-way functions. They both take arbitrarily large inputs and produce a smaller output. The important distinction is that cryptographic hash functions require collision resistence while fingerprints do not. The trade-off is that hashes are slower than fingerprints to calculate. So for large amounts of data, use fingerprints. For security-critical applications, hashes. Or both, starting with the faster fingerprint and using it like a Bloom filter. This specific case is a little confusing because MD5 is a cryptographic hash function used for fingerprints. MD5 is no longer considered trustworthy for cryptographic applications but can still function for fingerprints.
If you want the SHA256 hash you can use
ssh-keygen -i -e "SHA256" -f yourkeyfile.
If you and your friend are using out-of-band communications to verify your keys then good job. Just use the fingerprint provided by