Accessing Encrypted Local Backup

I have a question in regard to how encrypted backups work.

I downloaded iTunes and then backed up Phone A. During this process it asked me to create a password to encrypt the backup. I went ahead and created a password.

Later on, I backed up Phone B onto iTunes (I was not prompted with anything regarding passwords).

After that, I was setting up Phone C and selected "Transfer from Mac or PC" in order to restore the phone from Phone B backup.

I connected Phone C to computer, selected restore, and was prompted for a password. I tried using the password I setup for Phone A but it kept being rejected.

So is the encryption password it is looking for specific to each phone? Phone A is my phone in this scenario. Phone B and C are a friends phone I was helping setup. Is this password it is looking for, some password that was setup by Phone B when it got backed up another time on a different computer?

Thanks