Deciphering the different forms of kk, as destructautomaton asks, you look first at the overall structure of the teaching syllabus. You will see a great amount of combative utility stripped away in the phys ed courses(although the veneer or presentation might be rough and tumble or tough, taught by a military person or done in a temple or whatever). There will be a general focus on "forms" or dancing the weapon and doing repetitive two man drills(and you will see competitions for that throughout the year as well). Presentation and accuracy of presentation is paramount along with aesthetics. You will have a great structure and progressive learning map well laid out for teaching and training. We sometimes refer to this new format of training krabi krabong as new kk, as opposed to old or functional combative kk, to help distinguish it further.
In the phys ed format as well, the live steel, especially sharpened steel are generally not stressed and there will be a exchange of using wood mostly then steel later (as well as for demos), no actual test cutting or learning to cut into, through and at a person and how to develop and those shots along with dealing with blood and killing will be discussed or demonstrated. In combative kk, forms are much later in the training and are used for presentation at special events but mostly for centering(meditative), footwork and the many footwork patterns are stressed, stance and guardwork, high to low patterns, learning to deal and handle a real steel sword, drilling on developing speed and power, generally targeting right away is to disable or kill the opponent, the mind set and meditations that lead one to survive a combative situation, two man is less what i call "riding the rails" where two people face off and go back and forth and striking into a sword is rarely seen, the combative footwork patterns are stressed within those drills and they tend to be shorter and more explosive.
Thats a general overview of course there are different systems and training evolutions for each. Some phys ed might incorporate a bit more of the contact side especially in the college courses where they will actually spar like in the combative form. Likewise you might see the use of "soft" swords or wood covered with form, in combative forms to teach the eye shots and various other sensitive target shots, and any other shots that cant realistically be practiced into the target with wood or steel.
Its impossible to condense all this down into something overly simplistic since the role and evolution of phys ed-- what it means and how it is interpreted by the Thais and the thai teaching system is important to understand as much as the training itself and why combative has been pushed out and away much like the earlier bare knuckle systems were generally abandoned in the face of the new evolution toward ring Muay Thai. We see this new format of old muay forms known as muay boran in the same light, where aesthetics and presentation are paramount over fighting, understanding utility or function preparations. Even within the authentic systems or surviving systems like muay chaiya, we see they have abandoned any type of function or competing to strangely fight over aesthetics, hierarchy of teachers, and exact replicas of movements without any life or force thus antiquing the system. I mention this only because these are recent things in muay and muay boran and its something that has already happened to kk and the old weapons systems so much so that one cant even tell anymore whats real.
We would have to go into a system by system analysis to show the very intricate differences which once shown in detail will produce an enormous amount of clarity and understanding.
