If I had to break it down it it would be recreational diving, military, or commercial diving.
I would put instructors in commerical diving, because you don't need to be a commerical diver to be an instructor. I'd put them into the recreational diver group. For example, IMO recreational divers can be mixed gas divers, teachers, cave divers etc. Scientists can use recreational or commercial diving depending on what exactly the project demands.
"Recreational" isn't nessesarly the best choice of a word. I think thats why there are all these other titles out and about.
I agree with you that the term "recreational" has been ued incorrectely to lable the basic open circuit sport/vacation diver vs. anyone with more advanced training that uses it for a hobby.
I also agree that Instructors and paid Divemaster/Dive Cons should be in the commercial diver catagory.
Where I do not agree with you is that there is a very defined classification of four industries in the field of diving here in the United States that works really well to seporate the reasons for the diving. It is based, unfortunately, on the legal definition by our federal labor agency and is therefore somewhat mixed when it come to SCUBA instructors and the scientific community.
Anyway, I wrote a long definition one time either here on ScubaBoad or the DiveMatrix, I can't remember which, that went some thing like this:
Commercial Diving is the act of working underwater for compensation unless done so for the following excepted groups;
Diving for recreation or hobby is an exception to the rule and the instruction of others in the skills and equipment to do so, even if for compensation, is excepted from the classification of commertial diving.
Diving to preform research and scientific study, to include the use of small hand tools, is exsmpted from commercial diving only if done under a formal diving control board of qualified individuals that sets the rules for such diving and activities.
Military diving is exempt because you just can't argue with someone that has more fire power than you do.
Now, just for the sake of convenience the Public Safety Diving community has been broken off as a seporiate group from commercial diving because they do light diving work, for specialized reasons under the direction or athority of fire/police/rescue agencies that do not fall within the norm of the commercial diving industry and typically they use recreational scuba equipment to perform their tasks.
Technical diving in my opinion, once again, is any diving equipment, technique or diving outside the limts set under the typical recreational diving certification agency reccomended limits that is pretty typical between PADI, NAUI, SSI, YMCA, CMAS, and BSAC that state open circuit scuba, within the No Decompression Limits of the table you are trained to use, no deeper than 130 feet deep (39.6 M) where the diver can make a direct ascent to the surface (i.e. no hard or self imposed overhead obstruction to the surface).