whats the difference between profit center and bussiness area?

Profit Center - The profit center view shows the various 
internal areas of responsibilities. Objects such as cost 
centers, materials, etc can be used for profit center 
analysis. Profit center can be used to determine the 
revenues, costs, and profitability for specfic areas of 
responsibility.

Business Area - Business area forms an important part of 
external reporting. Analysis of various segments, product 
divisions, regions etc is possible using business areas.