SSL fingerprint does not match

I checked the fingerprint for my Postfix SSL/TLS certificate like this:

openssl x509 -in public.cer -noout -pubkey | openssl pkey -pubin -outform DER | openssl dgst -sha256 -c

But when I obtain the fingerprint for the mailserver from my local machine

openssl s_client -connect my.mail.server:587 -starttls smtp < /dev/null 2>/dev/null | openssl x509 -fingerprint -noout -in /dev/stdin | cut -d'=' -f2

I get a different fingerprint. How can that be?

Thanks, Jan