Many people will tell you that Business Intelligence and Business Analytics are essentially the same. They are quite right. Business Intelligence is an older term and, therefore, also a less confusing one; CIO defines it as an umbrella-term that refers to a variety of software applications used to analyse an organisation's raw data. In this, we can already see the two disputed terms merged together, potentially causing confused and frustrated IT learners to pull their hair out.

Nonetheless, the definition stands. Business Intelligence is simply the umbrella-term, which carries Business Analytics with it as a function.
The reason to all of this confusion around the terms is simple; BI is an older term and, like everything else that is old, it got dismissed as old fashioned. Introducing BA as the new term, they convinced themselves that it was more innovative and actionable. In the IT world, you will surely meet many who has specific opinions about the difference between the two terms.