What I got is,

In BI, you already aware of patterns in Datasets.

In case of BI you have Question with you and you are looking for

Answer to that Question in the Datasets.

Ex : "Give me a breakdown of last month’s sales by salesman in the

poorest performing region" is question asked by Business, and

in response to this question you will generate some Report in BI

tool.

In Data Mining, you like to see hidden/unknown pattern in Datasets.

here you don't have Question with you.

Ex : Buying behavior of customers.