So what is the difference?
In the most basic sense, business software is any software that helps a business operate more efficiently. This can be inventory management software, customer relationship management software, accounting software or any of the myriad types of business software out there.
Enterprise software is a type of business software that is created to serve a certain type of business. Enterprise software is meant for large businesses that require software that can scale with the needs of the business. Enterprise software, therefore, needs to be more powerful than the software sold to smaller businesses, and may come as part of a package including the hardware upgrades required to run it.
So, while business software refers to all applications that help manage a business, enterprise software is a specific type of business software meant for large organizations that need powerful software that can be easily implemented across the organization.