This is an ongoing reconstruction of a popular article I wrote years ago on the Aikikai's use of Omote and Ura examined from a historical and political perspective. I found much to respect out of the different schools I researched.
Gozo Shioda started with Morihei Ueshiba in 1932, the year after the Manchurian Incident. Kenji Tomiki had been a student of Ueshiba for about six years, and didn't leave to open a school in occupied China for about four years to come. Morihei Ueshiba would continue to be a Daito Ryu student in good standing until 1937. Prior to this, Shioda's father had been a Kendo and Judo instructor in his own right and Gozo Shioda studied these arts too.
After Shioda's time serving during the war, he returned to Japan in 1946 and spent months searching for his family in Kyushu. He did return to study with Ueshiba in Iwama for a month, but he needed to earn a living in post war Japan. He started to teach Aikido in 1950, and worked for a shipping company in Yokohama. In 1954, he won the prize for Most Outstanding Demonstration in the All Japan Kobudo Competition. He was able to take this opportunity to get sponsorship to open a dojo and founded the Yoshinkan Aikido style in 1955. He adopted the name of his father's Judo dojo for his own school. Two years later he developed an intensive training course for the Tokyo Metro police department called the Senshusei.
From a young man during the war, to running a post war security firm, to working as a law enforcement trainer; Shioda Sensei had views on Aikido that do not resonate with many Aikikai westerners. From Wikipedia: Shioda viewed Aikido as being "not a sport but a budo. Either you defeat your opponent or he defeats you. You cannot complain that he did not follow the rules. You have to overcome your opponent in a way appropriate to each situation."
For all the machismo described in Angry White Pygamas (written by a British man who took the one year long Senshusei course) and the focus on combat effectiveness, Shioda achieved something that far too few other Aikido teachers achieved - he went his own way, AND stayed on good terms with the Ueshiba family. He continued to credit Daito Ryu and Takeda Sensei as the primary source of Aikido techniques as he became a famous teacher in his own right. Able to give amazing demos and demonstrate breathtaking skills, he never claimed magical powers or advanced spiritual growth. He openly stated all of his skills were attainable, and that they were the result of dedicated hard work. Unquestioned as an authority on Aikido and as a martial artist, the development of his association was cordial and not associated with the competitive acrimony that too many other organizations would see come to pass. In this, he achieved something that other "more harmonious" organizations failed to do. Nevertheless, this system was not developed to be all things to all people nor a spiritual path.
The language of Yoshinkan is different than the language of Daito Ryu. Ikkajo is no longer a catalogue of 30 techniques but instead refers to one technique. Also, while a Daito Ryu kata apparently refers to both an attack and a response (ie Karaminage refers to a technique I learned as Mune Dori Menuchi Jujigarame, both Uke's and Nage's roles are determined by the Daito Ryu name), Shioda would name a technique in a fashion more familiar to Aikikai people - the attack, then the response, and then the variation ie Shomenuchi Ikkajo Osae Ichi.
I have not seen anywhere that Shioda referred to Omote and Ura. He did use Ichi and Ni (1 and 2) for variations. Calling different variations "1" and "2" is a very simple approach, but this also leaves the possibility of other variations. Or, fewer. I first started this bit of research over the USAF adding Jujinage Omote and Ura, Kotegaeshi Omote and Ura, Tenchinage Omote and Ura, and Kaitenage Omote and Ura to the test requirements. While I know there are multiple variations of some techniques, I couldn't tell what variation was being called Omote or Ura, nor could I see why. I found groups like Yoshinkan did not insist that there was a Variation 1 or Variation 2 for every technique. Some techniques are 1 to 5, some just have one.
This is in keeping with other older generation non-Yoshinkan teachers like Shirata Rinjiro who had three categories of Iriminage (in addition to Omote and Ura) or five types of Shihonage (including Omote and Ura). I see Aikikai teachers are aware of the different movements, but they either don't name the variation, or the variation in question just gets arbitrarily assigned to one of our two categories. Some get associated with the teacher, "Today we're doing it Bill's way." While Ikkajo (1) and (2) bear some resemblance to Ikkyo Omote and Ura, this is not true across the board for all techniques. Aikikai does not have a way to communicate these extra variations, nor do we categorize them that I am aware of. So, 1, 2, 3...not only is more specific but also lends itself to greater numbers of possibilities than Omote and Ura.
No particular definition is required of variation 1 or 2 in Yoshinkan. The response is not necessarily linear for variation 1, nor necessarily turning for variation 2. The different variations are not always intended to mirror each other.
The defining difference seems to be how Uke is attacking. While Katate Dori Ai Hamni is a specific attack for Aikikai, the Yoshinkan system will divide up variations based on if Uke (Tori) is pushing, pulling, opening, closing, stiffy sitting in one spot, lifting up, sinking down, etc. This becomes an Uke-centric approach to training - throughout training, the student is learning to respond to very specific attacks from Uke. Uke helps a very clear reflex.