good answer, thank youI'll take a stab at this for the sake of discussion, but please note (again) that I'm a relative newbie and will of course defer to those with more experience and better accomplishments.
So, to the best of my knowledge:
-- There are individuals (and some schools) who have established "official" systems for training particular sports or exercises, sure, but in the universal sense of a system that all marker/clicker trainers adhere to? I don't think so.
The only universal part of marker training is that a marker signal (for simplicity I'll say a "click" but of course the exact marker can vary, and many trainers use both marker words and clicks depending on what is being taught) is given at the moment that the dog is doing something correctly, and then that click is followed by some form of positive reinforcement (usually but not always a treat or toy).
Beyond that, specifics can and do vary widely.
-- It depends how you define "correction." Some trainers use both clicks and physical punishment (prongs, e-collars, etc.); it doesn't mean they aren't using marker systems. Some trainers use "no reward markers" to signal when the dog has done something wrong, and then reset the exercise or, depending on the situation, possibly impose some form of non-forcible punishment (like a time-out). Some trainers don't use anything and just ignore unwanted behaviors (Emily Larlham comes to mind, and I think Susan Garrett does this too? but I'm not as familiar with her approaches); in that scenario the only "correction" is that the dog does not get a reward.
I would consider all of the above to be using some form of marker training to at least some degree. There's nothing about clicker training that is inherently incompatible with the use of either corrections (including verbal corrections/no reward markers) or physical punishments, although in practice most people who call themselves "clicker trainers" don't use the latter and sometimes also avoid the former.
-- I don't believe any single person can be given credit for inventing marker training. People refine it and add new innovations and improved techniques all the time, but the underlying concept of signal-reward (or, I guess, signal-punishment) is something that people have probably been doing in one form or another as long as they've had dogs.
I feel like all of this is surely stuff you must already have heard before, as training discussions are doubtlessly old hat on this board, but like I said: for the sake of discussion, there are my thoughts.
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