According to Mary Thomas's Dictionary of Embroidery Stitches (1935): "The term 'flat stitch' is sometimes found in old embroidery books as referring to any embroidery worked in such stitches as satin, long and short, brick stitch and so on, all of which produce a 'flat' smooth effect."
A very basic looped stitch with many variations.
Open Loop Stitch, Tied Stitch, Y Stitch
A drawn fabric stitch that reverses to Cross Stitch. When used for an area larger than the typical single line, for filling or a border, Four-sided Stitch has been called Four-sided Border and Four-sided Stitch Filling.
Four-sided Openwork Stitch, Square Stitch
Stitch a line of Outline Stitch and when the end is reached, go back the other way, following the contour of the Outline Stitch, with small even Running Stitches. Go back and forth with the Running Stitches as many times as desired.
A primary embroidery stitch, the only variations being the number of times the thread is twisted around the needle.
French Dot, Knotted Stitch, Twisted Knot Stitch