Prepaid
The Prepaid option means that the account tied to the profile will be assessed the freight charges. This account needs to be properly registered in the system via the Carrier Administration section of the admin screen. A prepaid account is always required when shipping through ShipStore, even for third party (acts as a fallback account in case the bill to refuses charges).
Bill Consignee by Account
Also called Freight Collect by some carriers, this option allows you to bill the charges to the ship to. This option requires you enter an account number so the carrier can validate the account before processing.
Bill Consignee by Address
Also called Consignee Billing by some carriers, this option is similar to the above option, however you do not need to enter an account number to process a shipment using this selection. That said, you need to make sure the customer has this feature enabled on their account before shipping using the Address option. If not, all charges will be passed back to the Prepaid account.
Third Party
This option is similar to the Bill by Account selection, but requires that you also enter the Bill To address for the shipment. This is useful when billing either a corporate headquarters tied to your ship to, or if you are shipping on behalf of a customer.