Ok, I'll try to answer from perspective of a similar style, Aikido. The concept you mention is similarly defined in both styles - although to be honest, this exists in all styles. Let me explain.
It all has to do with "atemi". In Aikido, atemi is the act of creating a diversion. This diversion is used in order to get the attacker to do something else - usually, something expected so that the defender can defend against the known response. It has other purposes, but for now, I'll just focus on this part.
So imagine your opponent is coming at you (a bear hug, or is reaching for your throat with one hand and in the other he's got a fist or a knife he wants to introduce to your face.) Your atemi is to throw up a strike to the eyes, for example. The idea is to get him to flinch, and even to grab at your hand. (Off topic, but this is where the "here, grab my wrist" syndrome begins. It's legitimate, but there's more. Read on.)
So let's say he flinches, and to avoid having his eyes poked out, he jerks his head backward - to the point he falls down. All because the defender stuck his fingers up toward the attacker's eyes.
That's the theory, anyway. But let's look at what happened. First of all, such a scenario is unlikely to succeed all the time. The attacker is probably pumped with adrenaline, and is not likely to notice your fingers poking toward his eyes; that would require a micro-focus on a relatively little detail that would, in practice, go unnoticed were the esteemed attacker is drunk, high, on roids, mentally unhinged, uber-angered, injured, or overconfident in his size/strength/speed is better than the defenders. Whatever the case, it is likely that this maneuver won't work. At least, not for this specific purpose. It can work, but it's not likely. It is more likely to work in a controlled environment where said alcohol, drugs, steroids, etc is not a factor. In other words, where the pretend-attacker is probably competently protective of his eyes or throat.
What's more is what the outside observer sees. The observer notices that the defender stuck his hand out, and the attacker backed off. (Also off-topic, but this is where the famous no-touch knockout charlatans capitalize and over-dramatize this effect).
What the outside observer has noticed is that the defender used some sort of internal energy to ward off the attack. It's like the shell game which has the observer thinking the defender has this power, when in reality, it is mildly retained in the attacker.
Looking at this objectively, we can readily see that there is no outside force or internal force or whathaveyou. Do you believe that such Jedi mind tricks and dark forces work? Well, don't let me be the one to keep you from your journey to explore that. But I can say that in this scenario, the mistake (remember, there are many, but I focus on the one related to your question) is to attach a wrong explanation of what is seen, and not use one's intelligence to see the situation for what it is: no transferal of energy, but rather, cause one to use his own energy (and fear!) to ward off an attack.
Did I mention this exists in other styles?
Yes, we see this in boxing. It's called a jab, feint, or fake. You know, to get the opponent to lift his guard so that you can get around it. We have the exact same thing in taekwondo, kickboxing, karate, muay thai... it's ubiquitous. We just don't call it "atemi" all the time, and for the most part, it seems only the Japanese have turned the concept into a science. But it is there. Even Sun Tzu talks of it in The Art of War (see examples in chapter 3, "Attack By Stratagem"); and so does Bruce Lee in his Tao of Jeet Kune Do (“Pretend that you are weak, that he may grow arrogant.”)
Don't fall for the invisible force crap. It doesn't exist. Do you believe what you see whenever a magician gets up on stage? That there is a life force somewhere that lifts the assistant in the air without strings? Of course not. Every magician relies on deception. Physical mechanics hidden in plain sight to make you think there is magic. Of course, even the most intellectual among us like to see a good magic act, and know full well that there is no magic. We like to be fooled, knowing we're being fooled. And because our lives (and eyesight) is not in jeopardy, we gladly accept it. But it is no different.
So I said all that to say this: the internal force you talk of is not possessed by YOU. Rather, it is possessed by HIM. It is the no-touch-knockout guy (the magician) that tries to convince you that he's the one with the power.
You utilize that internal force by creating a diversion (atemi, fake, fein, etc). If he were dead, unconscious, blind, or unaware of your presence, then none of this would work, because he cannot see your diversion. If he were high, drunk, or enraged, this would not work, because he does not have the mental faculties to react in a predictable way, or even understand the diversion you've placed before him. Ever try to create a diversion for a dog throwing him a ball? An astute dog doesn't fall for the diversion. A stupid dog falls for it every time.
Ah, and then you mention something about relaxed power generation. The Chinese have turned this into a science, they call it fa-jing. I believe you asked not to discuss this, as it relates to something physical (an explosive state made more strong because the whole of the body can focus all of the momentum in one direction; were the body to be moving, or be stiff or similarly hindered, fa-jing cannot work because the momentum is not channeled into one direction - it is scattered.)
Nevertheless, there are some (the charlatans and magicians) who tout this as some mystical energy created from being relaxed. It isn't. It's the explosive movement from muscles at relax suddenly being directed into one direction.