Engagement Rate or ER (here's how we calculate it),
Social Interaction Index or SII (here's how we calculate it).
They both illustrate how engaging your (or your competitors') Facebook Page is. However, there are a few distinct differences you should take into consideration when decoding their meaning.
First of all, ER only takes into account interactions with posts published by the page, while SII also includes posts published by fans on the page and interactions with those posts. This means that ER shows how engaging your content is, while SII shows how engaging your page is. So, SII spikes will indicate situations when there's an increased number of posts to page (and discussions around them), which usually means "a crisis" - service outage, promotion gone wrong etc. ER on the other hand will spike in situations when there is a particularly engaging piece of content published by the page.
The second difference is that SII factors in different weights for different types of interactions - comments are more valuable than likes, shares are more valuable than comments. So, if you publish a post that is particularly viral or that generates discussion, your SII graph will spike much higher than your ER would.
The third difference is that SII factors in community size and neutralizes it so that you can directly compare engagement on pages with very different community sizes.
All the above suggest that SII is a much more accurate index to describe engagement on a Facebook Page. Why do we bother showing ER then? Well, its formula is much simpler, which makes it easier to grasp. It has been used for years throughout different social analytics tools and it became standard. An imperfect standard, but still.
Let us know if this answers your question. If not, we're always happy to chat and discuss your social analytics!