IIPA and DIPA mean the same thing. We picked IIPA in the Style Guidelines in 2004 when they were relatively new to the market, but it seems like the market has settled more on DIPA. So it could change in the future. If you read the comments of the guidelines, it basically says we just picked something arbitrarily since we needed to call it something and there didn't appear to be standardized usage in the industry.
No matter what name you pick, people will always pick something else just so they can say they are different and special. Expect it.