I´d agree that the strict definition of the word hogarthian applies only to gear.
Sometimes when I ask questions about a rig (always curious) I get the "better divers than me doing more advanced dives than me told me that this is the way you should configure yourself". Maybe it is a line people use who don´t want to talk about their gear but to me it sounds like a "cop-out" and to my mind is exactly the kind of thing that, no offence, leads to people wearing pink snorcles, split fins and all manner of danglies...
However, it seems likely that someone who´s spent enough time and effort to "develop" a hogarthian gear config has also given some thought to things other than gear. When I see someone in a hogrig I infer quite a few things about other than gear. I´ll mention a few examples to explain what I mean:
-Longhose: The "only" reason for a longhose is to make airsharing easier. Wearing one indicates to me that the diver has given some thought to the problems and situations where airsharing could be necessary and has taken steps to simplify the process. I´d expect someone using such a hose to be proficient and ready to initiate airsharing should the need arise. Also changing gear from "the norm" to a longhose indicates to me that the diver takes his "buddy responsibilities" seriously and I´d expect him not to be a "same ocean"-buddy.
-Can light/similar: A big light might just be a case of "this is a cool toy" but coupled with the rest of a "hogrig" I expect that the buddy will be able to understand and use his light to communicate, that includes passive communication (keeping beam in line of sight). Once again this "commitment" to communication is an indicator of the importance the diver places on the "buddy system"...
I could go on and on about almost every piece of gear but I think you get my drift. In my experience I very seldom end up dissapointed when I infer these things about someone with what, to my mind, seems like a reasonable setup...
Basically I expect a hogarthian buddy to be a "good buddy", someone who feels that people who enter the water together should exit it the same way, that problems should be solved underwater (as much as possible), that a good plan and good awareness is a good way of insuring a good and safe dive, that skills aren´t something you "learn" to get a c-card but something that enchances safety and minimizes risk on every dive, that silt is bad and should be avoided etc.
How does this differ from a PADIOW-buddy?
PADI OW, at least in real life, doesent teach this. Mostly it seems not even OW-instructors learn this.
How does this differ from a DIR-buddy?
I honestly don´t know, I´ve never dived with one.
If I was feeling provocative I might reply that some DIR-divers tend to give answers like this one: "better divers than me doing more advanced dives than me told me that this is the way you should configure yourself"...to me the poseidon thread on TDS is a good example of this attitude...
