What are the main differences between a core banking system and a billing system?

Firstly a core banking system consolidates financial and non financial information from across the bank branches into a centralized location to enable a bird's eye view of the bank.

A billing system manipultes the data available in order to produce customer wise output in the form of amount to be billed etc. Basically Core banking takes information in while billig system sends information out.

Billing system is not specific to banks whereas a core banking system is for banking purposes only.