Context: I am a PhD student in mathematics currently applying for tenure-track positions at small colleges throughout the US.
In general, most openings I've seen are asking for what they've termed a "Teaching Statement," while the remainder ask for a "Teaching Philosophy." Is there a difference between these two documents? If so, what is it?
I've posed this question to a wide variety of people (colleagues, panels, etc.), and they can't seem to arrive at a consensus. Some say that there is no difference whatsoever, whereas others say that a statement is supposed to be much more concrete and give more specifics than a philosophy.
I realize that this question was already addressed in some of the answers to this question, but I'd like to hear a little bit more detail, if possible.