I knew there was some variation in the way the stitch looked if I worked in different directions, but thought it had something to do with the way the yarn was plied. (And that may indeed have something to do with it, but not in the way I thought.)
I pulled all my stitch books and looked up both Stem and Outline Stitches. Out of fourteen books, only two depicted them as being distinctly different. Another five noted a difference but said it didn't matter as long as you were consistent. Five more had just one or the other, and two had neither!
And oddly enough, the usually comprehensive Mary Thomas didn't even mention it at all, perhaps since she classified her stitches by genre rather than method.
It's clear than there is a huge range of opinion where even the simplest stitches are concerned. And in seeing the many different ways the instructions are worded and illustrated, I don't think one is any clearer than another. It's a difficult thing to depict a kinesthetic action in words or diagrams. Video or even learning in person should be better, but might not be depending on the individual involved.
And of course,in the end the name doesn't matter a bit. What's important is that you get the effect you want, however you contrive to achieve it.
I got caught up in all this minutiae whilst working away on the bears, and thinking that what I am doing is mark making, not crewel embroidery. My stitches are really quite willy-nilly, and although I consult stitch directories for inspiration, I don't actually follow them that closely. My process, what I consider one of translation, is based more on the material I am working with than formal technique. It might sound banal, but is actually kind of a revelation for me.