A management information system (MIS) in simple terms is a system where all the organizational data and system data is collected on a historical basis. It can be present as a data warehouse that gathers data from different sources on a continuous basis.
The objective is to obtain customized reports from the system based on requirements of managers. The main purpose of the MIS is to give managers feedback about their own performance; so that top management can monitor the company as a whole. Information displayed by the MIS typically shows “actual” data over against “planned” results and results from a year before; thus it measures progress against goals.
Business Intelligence (BI) covers all the processes from the source data to the final reporting. From that perspective, MIS is just a part of the whole BI framework. It encompasses data staging, data warehouse, reporting tools etc.
In terms of reporting the data to the management BI is an advanced process of reporting which is applies more analytics and visualization techniques over the data for easy consumption of the users.