Hado no Chikara is the equivalent of saying "The Force"
It's a blanket term for a technique/power.
Satsui No Hado is the equivalent of saying "The Dark Side". It is a specific methodology of drawing on a specific technique/power.
That said, the proper method of harnessing Hado no Chikara, as with the Force, is NOT with the SnH/Darkside. Doing that is inherently negative and imbalancing to the user & nature. It is an affront to the concept (though still potent). Hado No Chikara is the motion of life force within all beings and the cosmos...it is the harnessing of that universal energy. This is no different from the Force. Snatching up that power and directing it with personal malice, greed and desire? That is bad. Always. Gouken's methods are inherently correct just as the Jedi's valorous, principled use of the Force is inherently correct. Notice neither Gouken nor Jedi suffer the kind of rot, degradation and corruption of Akuma and Dark Jedi/Sith.
When you pervert nature to gain power...you pay. This goes for Bison as well. His power corrodes his body. It bursts the seams of his mortal frame forcing him to turn to technology (unnatural means) to attempt to counter that process. Just like Emperor Palpatine making clone bodies in Dark Empire.
Mu No Ken is a different thing all-together. That is why someone like Gen can use it without having any background training in the principles of the Hado (Wave motion technique).
Mu No Ken is a spiritual and mental state that a martial artist can achieve. Any martial artist (in theory). It is not tied to specific fighting techniques...but it CAN be used in any fighting style with their techniques.
That said, a persons background & training might help them in achieving a state of Mu No Ken. Bison, for example, could not do this because his martial art is inherently based on selfish personal interest. Ryu's training has focused on valor and a higher spiritual calling for the purpose of wielding his fist...this makes it easier for him to divest himself of...himself and eventually achieve Mu just as Gouken did. Gen is such a straight-up bad ass with such unbelievable levels of training and spiritual awareness that he was able to achieve Mu against Akuma.
For parallels to my earlier comparison of Hado no Chikara/SnH to the Force/Dark Side...there IS a Mu equivalent in Star Wars.
Obi-Wan achieves Mu. He becomes perfectly one with the greater life Force of the universe...a part of it but still himself. He achieves immortality of the self by understanding that the self is a lie.
Yoda does the same.
Palpatine? He goes screaming into the abyss, never to be heard from again. The same will happen to Akuma. The candle that burns twice as bright, lasts half as long...or...in this case, lasts INFINITELY less when compared to oneness with the universe.
Here's a breakdown I've been considering doing for a while now...insight into this entire topic that comes from the best portrayal of SF as a coherent product: SFII The Animated Movie
Spoiler
The mantra Ken goes through with Gouken in his mind. Let's look at a few things about this entire scene because it is pivotal to understanding the martial arts philosophy that infuses Street Fighter.
First of all. Ken was crippled. Bison destroyed him as a martial artist.
"My legs...they won't move" - Ken
This was not anything but literal. When Bison discarded Ken he did so fully believing the attack would kill or cripple him. And he was right. "You don't seem very concerned about your friend...who's probably dead by now". Again, Bison is not being hyperbolic. He threw Ken at damn near terminal velocity (or more) into a goddamn stone wall so hard it left a dent. It would have shattered Ken's vertebrae.
And that's the key thing to understand. It did. The injury could probably be most closely compared to the damage suffered by Steve Austin in a match against Owen Hart where he got spiked onto his head. He also had limited mobility afterwards and took a long time to heal (and never fully recovered).
Ken drags himself to the edge of the battle, attempts to stand...and collapses. He then thinks back to his training...and touches Mu. In doing so, he is able to re-enter the fight and fight at 100% capacity as if nothing had happened.
Let's break down the mantra and what it means in full context keeping in mind the translation from the original Japanese is MORE than adequate enough for our purposes. And yes, there are differences between the two with the Japanese originally focusing more on harmony of movement and overt zen principles...but the message is the same. Perhaps later I can break down the Japanese dialogue and how it reinforces these same concepts but, for now, let's stick to what everyone is more familiar (save for ONE difference I'll mention at the end)
"Be prepared for the unexpected
Concentrate, mind and body as one"
"Be prepared for the unexpected" is inherently paradoxical. This is on purpose. It's a koan. A Koan is a Zen Buddhist riddle designed to point out the inherent flaws of using strict logical reasoning to understand the divinity of nature. It is EXPLICITLY used to provoke one towards the path of enlightenment.
Mind and body as one is the very essence of chi manipulation, gathering and use. We are not just "crude matter", as Yoda called us. We are a mind and a body and, through that synthesis, so much more than the sum of those parts.