Thanks, Joshua, that clarifies quite a bit and fits well with how I've heard it used in sword crafts (polishers, kinko, smiths, sayashi, etc.) often where there are also issues of lineage (in one sense or another). It usually seemed to be about personal transmission from one to another and not just "I study this or that" in a general sense. Makes sense. Thanks again.
Right. I probably should have mentioned this in my previous post, but while "deshi" and "monkasei", etc., mean "student", they are only used in describing one's relationship with one's teacher.
One could say, "I'm a deshi of XX-sensei." One could not say, "I'm a deshi of aikido."