Broke this from the "Future of Aikido" thread in order not to go O.T.
Ikeda Sensei shows a number of basic techniques using "ki" and/or "aiki" and/or "kokyu-ryoku" (they're all elements of the same basic thing) and a few were discussed pretty functionally in the now-defunct thread "Ikeda Sensei Demos of Ki". In a very real way, Ikeda Sensei can be viewed as trying to use simple demonstrations to focus on the basics of every Aikido technique. As Jon mentioned above, the three basics of every Aikido technique are: kokyu-ryoku, tai-no-sabaki, and ki-no-musubi. In other words, kokyu-power, body movement for correct position, and joining-together the two bodies into a unit. The examples discussed in the early parts of the "Ikeda Sensei Demos of Ki" are very simple examples of the 3 principles of Aikido, with emphasis on the use of kokyu-power.
Currently some people are using the term "aiki", but "aiki" is just a usage of kokyu-power. Kokyu-power is sometimes also called "ki strength". There is also a tendency to talk about using "internal strength" and "Internal Power", but in reality Ueshiba's nomenclature kokyu-ryoku (kokyu power) already covers the basic principle of "I.P.", "this stuff", "internal strength", and so on. In other words, a lot of the currently trendy terms are probably redundant, plus they tend to leave many people with the impression that some new or forgotten factor is being introduced into Aikido. Looking at Ikeda Sensei's examples, he is using kokyu-power as he moves into position with Uke to make a unit-body connection and then Ikeda moves the combined new unit with his center. When Ikeda Sensei joins his body to the body of Uke via a solid connection and moves his center/intention, that is "aiki". I.e., nothing has changed since O-Sensei laid out the 3 basic principles.
I agree with Jon that there needs to be some clearer definitions and I think (IMO) the place to start is with "kokyu". A lot of people in Aikido, a few years back, simply defined "kokyu" as "breath", but the actual definition as being an element of internal-strength has become clearer over the last few years. Come to think of it, there were a number of posts/threads getting more into the explanation of "kokyu" a number of years ago, but "kokyu" apparently didn't ring the bell, so a number of people are now chasing the term "aiki" without understanding that the core of "aiki" is actually "kokyu-ryoku". If there is going to be a discussion on defining the facets of Aikido, IMO the place to start is with the term "kokyu". Come to think of it, that seems to be what Ikeda Sensei is attempting to do.