Think about it like this: Verisign manages the .COM registry, a database of domain names, what registrar controls that domain, their expiration date of the domain and its DNS servers.
Verisign makes available a few very simple operations that registries can invoke on this database in exchange for specific payments:
* Add X years to expiration date ($fee times X)
* Change registrar of domain and add 1 year to expiration ($fee)
* Change DNS servers of domain (free)
You paid GoDaddy to invoke the first operation, GoDaddy paid Verisign the fee, and the change was made in the database.
You are now going to pay some other registrar to invoke the second operation, they will pay Verisign the fee, and the change will be made in the database.
Your payment to GoDaddy was for a single thing (make this update to the database) and they already did it. There was not going to be any ongoing activity on subsequent years, there's no reason for any payment to move to anyone else.
