I don't think adding additional monikers (e.g. mini-IR) to a rating, or even comparing the abstract attributes (e.g. mostly done by this or that kind of flyer) of one with another, is very useful. Surely a rating is about the priviledges it gives you? If you need to fly airways, you need an IR. If you want to do approaches in Class D, you can do it with an IMC rating or an IR. And so on.
Furthermore, a rating and even the rights it gives you can end up having little to do with your knowledge or ability to operate safely and efficiently. For a start there is the oft-quoted example of a pilot who rating wise is allowed to fly in a way which his currency would not support. Or how about an FAA IR holder in an N-reg plane who would get quite a shock trying to fly IFR if that person had no exposure to GA airways flights in the UK, just like a PPL who gained his license in the Florida would.
It's all about the rules (where and what you can fly as per your ratings) and your skills (absolute ability, skill, experience). I think the rest is just clouding the issue.