We have to differentiate between Shotokan/Shotokan and Shotokai/Shotokai. I will explain.
Roughly saying, there is an Orthodox Shotokan that remained away from competiion and another Shotokan, which was geared towards competition. This one we can refer as Nakayama..s practice.
There are differences between both practices. Now for you to understand, the orthodox Shotokan remained basically in the Shotokan Hombu Dojo. Nakayama..s development took place out of the Shotokan Hombu, in the JKA (previous NKK) headquarters and abroad with great emphasis.
Off course, the orthodox Shotokan also had some Sensei that were abroad, by the time JKA followed their mind-set into competition.
Ever since its existance, Shoto-kai was just an association - as it is to this very day, and is, as always, in charge of the Shotokan Hombu... Also their members founded NKK...
As to these practices that we name 'Shotokan', there are differences, because one was centered in competition and by doing so, had to change the way techniques are performed, ex, towards hard contraction. That produced a practice that is visually broken into frames, very mechanical.
On the other hand, the orthodox Shotokan was softer, with more freedom of movements and does not contemplate the contractions at the level Nakayama..s students aimed.
There is also another very important difference. With quite rare exceptions, mostly of the sport Karate were students at the japanese Universities (mainly from Takudai) whereas the orthodox Shotokan was populated with the Masters.
So you have a different mind-set between both.
Master Egami was the successor of Master Funakoshi in Japan and concluded the development of the orthodox Shotokan from the Jutsu towards Do or Budo, as Master Funakoshi had told him to do.
These developments caused great impact among the orthodox Masters. Some of them adopted fully some of them just in part and others never adopted.
Anyway, in small amounts or in huge amounts, all the orthodox Shotokan that received the influence of Master Egami and/or the Shoto-Kai (Association), started to be called Shotokai. Not all of them, as Oshima Sensei in USA, Harada Sensei in Brazil, although in Europe Harada Sensei refers as to Shotokai, but with distinctions.
In fact, the very only one Dojo that during the 60..s and 70..s produced what may be called a true Shotokai practice, i.e. the practice of Egami Sensei, was the Tokyo Dojo - and here, we are not talking about the Hombu managed by the Shoto-kai (Association). This practice today is called Shotokai EgamiRyu® by which I am representative in Brazil and have legal rights for the name. Our Doshu is William Schneider Sensei.
This distinction comes from the fact, that in Europe, since Shotokai was first brought into Seminar by a 4th Dan of Master Egami, his practice started to have some mis-interpretation on the part or certain 'Shotokai' groups. They are named Shotokai today but do not portray the exact practice of the Master.
For instance, if you go about Youtube Sensei you will find lots of videos. Nevertheless you will notice that their movements are sort of 'gestual', with no real emphasis on speed, etc.
Well that is as far as it can be noticed an influence of Shintaido, which should be only one of the phases in learning the Shotokai way, but not its end.
So the Egami-ryu way is firm and energetic, always seeking for freedom of movements and speed, high speed. It seeks combat, opening and efficiency.
That means that the Egami-Ryu is like the Karate of JKA? By the heavens, NO WAY!!
It is a totally different world.
Let..s remember that, JKA had, since its depart into sport, better saying even before when Master Funakoshi along with his Seniors, perceived the trend into competition, the transmission was broken. Nakayama for exemple, spent many years in China, exactly the years that Karate in Japan was in open development by Yoshitaka Sensei. Nakayama Sensei lost valuable years of transfomation, he missed a lot and when he returned, he could not understand what he was seeing. Under Yoshitaka Sensei, the practice of Master Funakoshi went beyond his recognition and level.
Right here, a transmission was lost, because Master Funakoshi practice had left the square movements. Master Egami only sky-rocketed that and deeply enrooted the practice in Budo according to Master Funakoshi firm decision.
We should not forget that Master Funakoshi had already set his mind in that, re-confirming his will for Karate upon the time he re-founded the Shoto-kai Association, in open and clear assertivity against all the Kohai that was misleading the practice into sport and he, O..Sensei, never returned to NKK(!).
We can say that Shotokairyu has its line rooting from Funakoshi-Yoshitaka-Egami-Schneider (nowadays) or very close to this.
There are a number of diferences between the practice of Master Egami and that of Nakayama..s.
Nakayama could not learn everything that was in the practice of Master Egami because Egami Sensei belonged to the Seniors group, therefore the group of Masters that made the research for developments.
He belonged to the University group, not to the researchers, and therefore his activities had to be very over the surface because of time avalaible. Time was a main issue when dealing with students, so the number of Kata was lowered for example, practically no bo trainning or kenjutsu, etc.
Even Shotokai groups have problems with that when they inherit the same number of Kata because they offspringed from the University side.
As to Kata there are some examples that Nakayama..s lineage makes it wrong, some with an ending improvised or sort of, but was never taught that way. And why they do it that way? Because they did not learn it(!).
So mostly of these things either for Shotokan or for other Shotokai groups can only be found in the Egamiryu® because they are linked to Egami Sensei in direct transmission, with no constraints.
Now, you asked if the differences are related to politics. I do not think so in the very bottom line.
Master Funakoshi started to have pressures on the part of the University students, 02 years after his first presentation.
He wanted Karate as an expression of Bu and Do (Budo) and all his life devoted to this development. He was not interested in making champions. He was not interested in champions. He was interested in bringing life, real life. He was interested in Life as form of Art and Art as form of Life. Karate as the holy ground for that, better saying, Karate-Do.
Perhaps, he saw his Art when departing into the Sport-Do, felt sad, deeply regreting the lack of understanding, that spiritual side that was lowered to the level of plain muscle and nerves only. Surely he did not envisioned his Way being placed in a jail where two atackers relish a crown while others bet who..s the best. Money and amusement being one.
His Way was much more natural. His Way was non-violated nature, non-violent nature, just Nature. Men and Nature altogether as one, flowing to far beyond. So is the Way of Karate-Do.
If in the heart of some, politics kicks in, it is time for Bu.
'Bu inevitably steps in where humanity and justice fail to reach'.
'We should build the Way of Karate... for that it is necessary to go back to the starting point, to the teachings of Master Funakoshi'
Anyway, the reasons for the differences are many, but certainly the vision of Karate as Budo Art was the ball game. The understanding of this as well as the clear definition of what Budo is and means for man, made the difference. Even towards technique.
You see, many Masters of old told that Karate had left Japan void of Budo. And for that, other problems arouse for the comprehension on the part of the occidentals, i.e, the language itself.
Some learned, but in general the mix is with helenic conceptions. Modern Japan is more akin to that day by day and true Budo survives, under resistance.
It is part of my assertion that Nakayama..s 'Shotokan' became so graphical because that was all that the students had in the beginning: Gestures and Commands. Budo explanation should be very difficult in a foreign language let alone living it. So this practice became too near the body level hence physical stress and mental stress.
In my view, it is sole stress.
More about Shotokai History (portuguese)http://www.shotokai.com.br/english-index.html