Most machine made scarves that look like double sided stockinette, and are clearly not two layers, are really a 1x1 rib (k1, p1, repeat). The purl stitches recede, and all you see are the knits.
(Also, The best way to edge these scarves is to slip the first stitch of each row to make a chain selvedge.)
Shaker knitting produces a similar effect, but the purl "valleys" don't recede all the way, so it actually looks like a varient of ribbing (which it kind of is). Also, shaker stitches eat up yarn like you wouldn't believe.
As for knit versus purl:
Look at the construction of the stitch. When you make a knit stitch, one side is a V, and the other side is a horizontal bump. When you make a purl, one side is a horizonatal bump, and the other is a V. Knit and purl are just variations of the same thing--when you're purling, you're making the knit stitch backward, or vice versa.
the loopy sides of garter and stockinette are different creatures--
So take a look at your garter stitch. Pull the piece vertically so you can see clearly--it's made up of horizonatal ridges. On side A, the prominent part of the ridge is the purl bump that's created when you knit a row on side B. The valley is the knit V you made when you knit a row on side A.
(f you were making garter in the round, where only the "right" side faces you, you'd have to knit a round, and then purl a round to get the ridges)
Now look at your stockinette stitch--you knit a row (right side) and then you purl a row (wrong side). All the knit rows, and the reverses of the purls make up the plain V fabric. All the purl rows and the reverses of the knits make up the bumps.
Pull the stockinette piece vertically, and note you don't have any of the garter-type ridges.
A lot of books don't explain this basic stitch construction, but they should. It's something that makes "reading" your knitting, fixing mistakes and generally getting better at the skill much easier to do. Some of the few authors that does explain this, are Elizabeth Zimmerman (Knitting without Tears and others), Maggie Rhigetti, and Priscilla Gibson Roberts.
Oh, for the odd numbered rows? It depends on the stitch pattern and how it's written, and which side you want to be "right". So if it's stockinette, any knit row is the "right side" whether that's row 1 or row 2, depends on which you did first.