Business Intelligence has been around for a while, long before the name appeared.
Basically, getting data in front of the user as information to base decisions.
However, Big Data has spawned because of the need to extract nuggets of gold from the mountains of data.
The data is not uniform. Instead it's humongous, scattered and cluttered.
So I would say the purpose of both BI (Business Intelligence) and BD (Big Data) is "Create Order from Chaos".
Simply put, our goal is to parse through all this information, structure it in a way that is comprehensive, in real time, to produce some level of value, ongoing.
Information, the new "man made oil / gold".
To be mined and harnessed.
Bought and sold as a commodity.
And the new gold diggers are the data miners and business intelligence developers.
Remember the Gold Rush of the mid 1800's.
Move out west and claim your fortune.
Fast forward to today, we search for gold in that heap of data, shovel optional.
I figure there's no more land on this planet to plunder.
Might as well create some artificial commodity.
And you can do that by creating some type of order out of chaos.