I never know to laugh or cringe whenever this topic surfaces on ScubaBoard ... but some years back, Cave Diver wrote a pretty nice article explaining DIR in terms most recreational divers can comprehend ...
http://www.scubaboard.com/forums/dir/44823-what-dir.html
There is only a little bit of equivalency between hogarthian and DIR, in that the former is a gear configuration while the latter is a systematic way of diving that utilizes that gear configuration. But DIR encompasses much more, as has been described by several posters already ... equipment, technique, and a mental commitment to standardization. It's predicated on the concept of "predictable behavior" ... DIR divers avoid the dreaded "instabuddy" by training in such a way that they are completely predictable and interchangeable ... you always know what to expect from a DIR-trained dive buddy, and they from you.
Like everything else in diving, there are advantages and drawbacks. It's a system that works extremely well for people who are "system oriented" thinkers ... and it feels very rigid and limiting to those who prefer doing things "their" way. Most fall somewhere in between ... and can adopt some of the ideas and techniques of DIR ... but because the system is designed as an "all or nothing" approach, there's a tendency to resent that they can't be part of the tribe without going all-in. The name itself also tends to produce some resentment, because of a natural tendency on the part of some to assume it means if you're not DIR, then you must be DIW. I take the attitude that it's a marketing slogan, designed to be somewhat controversial in order to get your attention.
Although it's a system that was initially designed to meet the needs of one specific project, in one specific locale, and one specific environment, it can be applied (or more frequently, misapplied) to pretty much any environment. That doesn't mean it's necessarily the best solution in those environments, nor that it won't be "overkill" in some of them ... but it works very well for those who are used to it in pretty much any condition they can dive in. Anyone who tells you it's strictly for "technical diving" either doesn't understand the system, or they're trying to sell you something ... but they are partly correct in terms of the environment it was initially designed for.
By far the most popular, and widely adapted DIR course is "Fundamentals" ... what started out as a remedial workshop and eventually got mass-marketed as a way to get introduced to this style of diving. It's a good class ... one of the best I've ever taken, despite the fact that I decided shortly thereafter that the DIR approach, while it offers many advantages, was somewhat limiting for my personal diving goals. Much of what I eventually became as a diver was built off the skills and mental approach I learned in that class.
And that's really the point I'm going to make ... whether or not you ultimately decide to adopt the DIR style, much of what it will teach you is adaptable to pretty much any diving style you eventually decide best suits your needs. It isn't the philosophy so much as the added perspective ... the answer to many of the questions about diving that begin with the word "why" ... that so many find useful.
And to put that into the context of your question ... DIR will teach you how to make good use of a hogarthian rig ... while just diving a hogarthian rig will teach you little to nothing about DIR. If you really are interested in understanding what it's about, avoid the hot-button terms like "religion" and "cult" ... those make for interesting internet discussion, but do little to answer your question. Focus instead on the "why" of what most diving education teaches ... and ask how this can apply to helping you become a more skilled, more comfortable diver. Question everything ... any instructor who can't explain everything they tell you in terms of "why" doesn't really understand it. The DIR instructors I know ... both GUE and UTD ... do a very good job with the question "why". You may ultimately decide that their reasons aren't compatible with your goals ... but the answers to those questions will benefit you in developing an understanding of what you want to do and where you want your diving to go. And that alone is worth the price of their training ...
... Bob (Grateful Diver)