Hello & welcome to the forums
There's nothing wrong with your NAS, nor have you done anything wrong so *don't* delete anything!
For connection purposes, and by design, Windows considers a machine name and the IP address of that machine as 2 separate devices. Therefore you're simply looking at the contents of the same machine but as 2 different users.
When connecting to the NAS via name, you are probably connecting as the guest user and so can see the default shares which are guest accessible (though this an be changed). If you were connecting as the user "Graham" you would see the share called Graham in addition to media and backup as it is only accessible to that user, and not the guest user.
When connecting via IP address you must be connecting as the admin user which gives you more visibility - "homes" being the share that contains all of the users private shares, and "c" which allows you to see all the shares ('c' is the name of the internal NAS volume - kind of like calling your PC drive your C-drive - and so contains all of the folders that are accessible as shares. Useful for moving data between shares)
Normally you would not connect to the NAS as admin and so never see "homes" or "c" - these are made accessible purely for administrative purposes
This might help you understand better - it is an article that takes advantage of this feature: http://home.bott.ca/webserver/?p=275
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