Does changing of adress have any significance when subletting?
No, if you sublet your housing with a permit, it doesn't matter if you are registered somewhere else while you are subletting, or that the person living in your apartment is registered there. Just make sure that all your bills gets to the correct adress, otherwise there may be a risk that the fee from the housing association or that invoices from the property owner is left in the mailbox.
Does an address change mean that you are registered in the new address?
There is a difference between getting mail forwarded and making a permanent address change. If you are going to sublet your place, it is usually for you to settle in that municipality and then you should make an address change and make sure that you get the right tax rate, benefits in the municipality that you reside in and more. Address change is easily done with BankID at Skatteverket.