In the "chinese understanding of ki", there are distinguished so many different types of ki, eachone having a name of its own.
I never experienced or read that concerning the "japanese understanding". Am I wrong?
Well, there are different aspects of ki, but the basic, fundamental ki is the same in both Japanese and Chinese understanding. The original idea that strength, health, etc., is a function of something called "ki" or "qi" is the basis of the theory which is used in both China and Japan.
How do you distinguish ki and kokyu e.g. when you breaht in through your feet and out through your eyes? What is ki, what is kokyu?
"Kokyu" more or less equates to the idea of "jin", for all practical purposes. It's the idea of a form of strength that is associated with the breath and breath-related training built around a trained physical strength-skill (jin). "Jin" is considered to be "the physical manifestation of qi". So when, for instance, Koichi Tohei demonstrates a ki test the ki test works because Tohei brings his ki to a certain area and when Uke pushes against Tohei in that spot, Tohei is difficult to move. I.e., there is no real difference between the ki/qi in Chinese theory and the physical skills you mentioned in Aikido. It's all the same thing.
Incidentally, it's probably clearer for some applications if you interpret the character for ki/qi as "air pressure" or "pressure" and you'll begin to see some of the relationships in "pressure", "kokyu", and so forth.