These two is different. Storage server is the host which provide destination storage to NetBackup media server.
Depending on storage type, these two can sit on the sit host. In general, storage server must be media server when you configure storage that NetBackup provides(e.g. AdvancedDisk and MSDP).
When you use OST storage, storage appliance become storage server - media server is not storage server in this case.

Cant I have a successful backups and restores without defining any storage server?

No you cannot have a successful backups or restores without defining any storage server

You do not need a Storage Server unless you use Enterprise disk, OST or De-Duplication Storage

Basic disk and tape require only a media server - so yes you can have successful backups to basic disk, disk staging and tape without the need for a Storage Server

Summary:

Media Server : the server that performs your backups to disk, disk staging, Enterprise Disk, de-duplication or OST

Storage Server : A Media server that use Enterprise disk, de-duplication or OST

Hope this helps

The blog referred to by Ashish Sharma  really explains it well - with pictures!

Thank you