Re: Budo renshu/budo keiko
Actually, it has always seemed to me that, as a rough analogy, "renshuu" would be "practice", and "keiko" would be "training." At least in a sense of similar interactions between the words. But of course "training" doesn't carry all the nuance of "keiko"; the Japanese imported the word "toreiningu", so obviously they also feel that "keiko" and "training" are distinct.
As to why Ueshiba Morihei chose "Budo Renshu" instead of "Budo keiko", the first thing to know is that while, in general, "practice" for most things is "renshu" while for traditional arts it's "keiko", the distinction is not a mutually exclusive one. "Renshu" can be a part of "keiko" Nor should one fall under the misconception of "renshu" being a weaker word. I think of it as a "lighter" word, used as it is in a broader context than "keiko". But at its core it still means "to polish what one has learned", and it's component kanji show up in other words of importance in budo contexts. Such as "tanren", and "shutoku" Indeed, as "keiko" is so commonly used to describe the physical training of budo, the use of "renshu" in this context probably served to emphasize the importance of continuing to polish one's own skills.