I got the impression that kokyu-ryoku didn't just refer to "breath power". One translation I saw was "abdominal breath power". In any case, do you think "kokyu" (not just breath) could be seen as IP while "connection" and the associated application of kokyu could be called "Aiki"?
1. Abdominal breath power
Is the pressurized breath that I referred to.
2. Connection as kokyu
Connection has to be trained-in you- prior to it having any appreciable effect on anyone outside of you.
3. To answer your other question
Breath training is part
of Internal strength. Connection is part
The qualities that you are training to connect tissue crosses over in everything. It gets much more sophisticated. In any event, there is a reason that aiki takes place in you first.
I choose to stop there because there is very little information I have seen offered by any teacher in Aikido to address a deeper study, and very little I have seen as evidence they even know. For that reason I can't really address who chooses what to train and why with their own terminology. I keep hearing "stories" from various people about their Japanese teachers who can do amazing
Who really cares? All you have to do is review every, single, thing, ever written or taught on film by the big top dogs in Aikido to see that when they were given the chance...there was nothing there to help us what-so-ever in regards to IP/aiki. Now that ..we...have chosen to teach ourselves... all of a sudden they are out teaching internal power and aiki as separate works. That may slide under most peoples radar, not mine. I think we need to do the heavy lifting and teach ourselves.