Style of aikido is a little trickier. On the one hand, I think a dojo that expects a 5'4" 125 pound woman to have technique that looks exactly like a 6'4" 250 pound man's is probably not a place where I would encourage anyone to train.
On the other hand, if both people are teaching at the same dojo I would expect them to both have similar explanations for *why* their technique works, and similar reasoning behind whatever body-type driven adjustments they make. (I suspect this is part of what Tarik meant by "principle-based" instruction.)
Yep.. in part, what I mean by principle based instruction is that the reason that things work remain the same. I have been in situations where things I've been taught or have taught directly contradicted other instructors. I don't mean appeared to contradict (that happens lots early on if not careful simply because of nature of this), but actual, real different and contradictory explanations for how/why something works.
Principle based instruction allows a 4'11 student (I have a woman in my dojo who is that tall) to have technique that works for the exact same reasons as a 6'2 man. It may (should!) look different, but the reasons it works are literally the same. If not, there's something wrong with one or the others (or both) methods.
Principle based learning relies upon testable principles that can be proven or disproved again and again with simple tests. It's easy for all of us to fool ourselves without constant testing of both assumptions and actions.
I believe that there is a huge difference between someone who is simply leading a class and a teacher. In an ideal world, people should start by leading a class and learn how to teach from their teacher. In practice, this ideal world has long been broken and there are many very senior people running dojo who actually know very little about teaching.
Personally, I think this is one strong argument for the mode of silently leading of class by demoing a technique and allowing everyone to work it out themselves. But this is not teaching.