Continuing with "Simple Knit-Purl Combinations", I've done a swatch of (bottom to top) Seed Stitch, Moss Stitch, and Double Seed Stitch, page 11.
As per Barbara Walker, Seed Stitch is worked on an even number of stitches over two rows, Row 1 beginning with a knit, Row 2 beginning with a purl. This ensures that every knit stitch is above a purl stitch and vice versa. However, in our teaching blind and visually impaired knitters, we have Seed Stitch worked on an uneven number of stitches so that the pattern is now a one-row pattern, always beginning with a knit stitch: much easier for them to memorize and not have to try and figure which row they're on. In any case, the resulting fabric is firm and flat and the same on both sides.
Moss Stitch, worked on an even number of stitches, is worked over four rows: essentially a k1, p1 rib for two rows that changes to p1, k1 rib for two rows. While still flat and reversible, it pulls in a smidge more than the Seed Stitch.
Double Seed is worked on a multiple of 4 stitches over four rows. This breaks down to a k2, p2 rib for two rows that changes to p2, k2 rib for two rows. The texture is very defined, and the fabric is flat and reversible.
All three of these stitches are good for borders, as they off-set the curling of Stockinette Stitch.