One in which an account is kept of promissory notes, bills of exchange, and other bills payable or receivable: it ought to contain all that a man issues or receives. Bill is useful to customer also for guarantee and warranty of the item. It is useful to accountability. Amount received, balanced or credited to customer. 

Register is to enter or enroll in an official list or book of public records. Its very useful to keep records physically safe in your register to see anytime in future.