Hi @jefrii
If I talk in layman terms, then i would say Proofs are the copy of the deliveries which is used to check the rendering of the email, contents and personalization. You use proofs to send it to yourself or clients for proofing your email. You can look here on how to send a proof.
Whereas Seed Addresses are the target list which is not included in the main target. Hence along with the main target they too receive the email when the campaign is launched. For instance, If you want to send email to a particular address but that address is not present in the main target which has been defined. So you can add that particular email address in your seed list and send them the emails too. Please refer the link for more information.
Thanks
Akshay