There are a myriad of "Tec" courses available nowadays. Some DIR oriented, like UTD\GUE, some may not be, but the instructors may have DIR backgrounds. PADI\DSAT, TDI, the list goes on. I like the definition Steve Lewis\Doppler lays out in his book. "Technical diving = more time in water". You do usually see Tec divers in doubles with one or more stage(extend dive time) or deco (breathing to speed up decompression time) gases, but it doesn't change the plain and simple. I don't have much 'overhead' time at all, and I see the technicalities that people get into that try to define cavern\cave, but it doesn't change your gas supply needs to increase, along with a safe backup supply you turn around\step out of the the water with, which usually equates to longer dive times. I never had done a 60 minute dive until my technical class, for example.
You mentioned CCR being "tec" - I still can agree, as from what I have read, CCR includes much more task loading and having a higher level of awareness over your gear, but with "Type R" or recreational CCRs being released now, it seems as they are quite literally hands-free, such as the Poseidon MK6 discovery (which, so far, is designed to only extend your bottom time, in sport depth limits. PADI is just now releasing their CCR class line, where you start with Basic, move on to Advanced CCR (sport depth limits) and onto Tec CCR courses (including staged decompression into the dive plan).
For some, the extra gear seems ominous and ruins the 'fun factor' of single tank rec diving, it takes time to get used to the added weight and trim characteristics, but after getting comfortable in the water with them, putting on a single AL80 after diving doubles for a week straight makes you feel like superman\woman!
During any tec course, before any dives a good instructor will make sure you are 99.9% comfortable with your gear configuration and the dive plans, and I know for the DSAT (the technical diving leg of PADI) Tec deep course, some of the first training dives are just for that, with depth limits of 30-60ft depending on the dive #, to make you feel acquainted with your gear, and to even start instilling good buoyancy skills for ascending\stop protocols with (simulated) staged decompression stops. I didn't know what my instructor meant about decompression stops being like a state of meditation until the last dive of my course. But it really is - you slow your breathing, you don't move\kick as much (in calm seas, at least) and you just become a floating point in a huge ocean. By then, the dives are basically fun dives with one or two small skills you show your competency in, without even trying\being asked. It isnt for everyone, but when you feel ready, I really recommend to try it! (If you don't want to go full tech yet, theres also orientation courses you can take to get you comfortable with using doubles, still in recreational depth limits)