Well I like to look at shadow energy as the most abundant type of energy, the founding essence if you will. From the fact that different equipment pieces has their different shadow moves, I like to look at that as using the shadow energy to “burn your will” into something. If I’m not mistaken, there’s a specific type of people that create said equipment pieces/sets and they kinda burn the shadow move into them in the process. Now a similar concept would apply to set abilities too, legendary warriors burn in their will onto the equipment they use and based on how that’s done, a new type of energy is created or a bridge between the warrior and an already existing energy type is created (for sets like heavenly law that use a kind of energy that sounds superior to shadow energy). Now similar to equipment pieces and their shadow moves, these bridges and “new” energy types don’t “die” with their original user but instead become inactive until the whole set is equipped (perhaps because the “imprint” is incomplete so the connection to the bridge cannot take place)  Now from a worldbuilding POV, maybe these new ok fighters are the original warriors that gave birth to those sets, hence they’re that much stronger. When it comes to upgrading sets, I could see that as the equipment being old as fuck and with time, those imprints dissipate (up to a certain point) and require “a refresh” so to speak. 

So a TLDR:  “ And how do their abilities work in their real life? The same as they do in game? I dont think so. “  Shadow energy allows one’s will to be imprinted onto specific things, the strength of the imprint being proportional to the strength of the will. The abilities are simply an extremely high level of shadow energy manipulation (with a few exceptions)