Call them what you like - rope halter, cowboy halter, natural horsemanship halter, resistance-free training halter or just plain training halter.
I tie 3 types of these rope halters-
Regular - to use for training or under your bridle for trail riding
Extra Nose Knots - also for training but with more pressure points - many popular trainers recommend the halters with the extra nose knots
My halters are made with sturdy 1/4" braided polypropolene rope of medium stiffness. (By this I mean the rope is not soft and floppy like some, but not wire-like like others I have seen. The nose band will stand on its own when placed on the floor) The overhand /fiador knot under the jaw can be adjusted to a somewhat smaller nose. (The overhand knot is more user friendly to adjust) (All other knots are double overhand knots-also known as blood knots) I have been making the poll strings longer to allow for growth, but they can be cut and singed back for a shorter look. As stated earlier, I have two options for attaching your lead rope - the overhand knot or the fiador. Both are equal in usage. It just comes down to personal preference.
I also tie a side pull halter / rope riding halter / headstall with one inch rings tied into the two side knots for hooking reins or long lines to. You can use this halter for driving, longeing, riding, or as a regular training halter. These are also made with 1/4" braided rope. Typically, these are tied without the extra nose knots.
I have used these halters to train my horses for years. They work great - I've never had one break. My animals have become soft and virtually resistant free. Try them - they really work. You will never go back to a web halter for training again! All of my halters come with satisfaction guaranteed.