Other experts are pointing out that with BI, you are looking in the mirror and using historical data to understand your business. The data might be from two minutes ago to two years ago; as long as it is telling you what happened in the past, it is BI. When focusing on business analytics, you are looking in front of you to see what might happen in the future - you are anticipating in what the future brings. This explanation brings more clarity to the terms; both methods provide you with insight into your business, but different kinds of insights.
The truth is, that the terms are insignificant as long as the business has worked out its most favorable way to leverage the information. Yet, professionals are still discussing the difference and holding on to their opinions. Take this new found information with you to the next one, end the discussion, and feel smug about yourself.