Whats the difference between storage server and media server?

Very simply (and I'm sure there are more detailed descriptions available):

• A media server is a NetBackup data mover. It manages the data movement between the client being backed up and the target backup device (disk, tape or whatever). 
• A storage server is a NetBackup entity that manages the backup storage (the MSDP pool you are backing up to for instance). It is not necessarily a media server (although it often is as well).

If you need more information have a look at the solution (and links) from this same question about 8 years ago (not much has changed in the definitions): https://vox.veritas.com/t5/NetBackup/Whats-the-difference-between-storage-server-and-media-server/td-p/540508

Herewith Veritas link to the blog mentioned in above post:
https://vox.veritas.com/t5/Protection/Master-Servers-Media-Servers-and-now-Storage-Servers/ba-p/776818