What is the difference between a Teaching Philosophy and a Teaching Statement? 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.
One of the confusing aspects of the various fields of academics is that within one field there can be many terms that essentially mean the same thing. People may try to state that there is a difference but normally the differences are so minor that it is essentially hair-splitting.

The difference between a "teaching philosophy" and "teaching statement" is basically the second word used in both terms. If there is more difference then this it is so nuanced that the average person would fail to notice.