The thread Kim linked should answer your questions as well as some you didn't know to ask
To summarize though, 'Hogarthian' is a minimalist gear configuration. There are variations of this configuration, but the basic rule is "take what you need and leave what you don't." 'DIR' utilizes a Hogarthian gear configuration with fewer variations (yes there are a few minor variations, though some folks seem to make a big deal of them
). But the gear configuration is only the first tiny baby step of DIR. It's a whole way of diving that includes teamwork, situational awareness, rock solid skills, contingency plans, gas management and dive safety. I found that once I put the whole package together, it made *all* of my dives a whole lot more fun, safe and relaxed.
Today I did a night dive with someone I'd never dove with before. He was DIR trained (RecTriox 'provisional'). After a very brief introduction, we planned our dive and dove it. Because we both had similar training, we knew what to expect. We dove to 110' for a stress-free, relaxing 61 minute run time. We were on the same page as to time spent shallow for time spent deep. We didn't review any communication signals at all before the dive and the few communications that happened were simple and clear. We were not elbow-to-elbow for the whole dive, but even when I was snapshooting pictures and he was looking into the end of a pipe or log, there was never any wondering where the other was.
Sure all of this can be accomplished without the 'DIR' training, but for most of us who have opened our minds enough to consider that GUE has something to offer besides ego and kool-aid, the package has been well worth the time and effort put into it.