satin stitch

a long, straight embroidery stitch worked closely parallel in rows to form a pattern that resembles satin.

Origin of satin stitch

First recorded in 1675–85

Little eyelets or satin-stitch dots are worked between the lines.

The Library of Work and Play: Needlecraft |Effie Archer Archer
The letter "A" of Figure 133 shows a good combination of satin-stitch and back-stitching.

The Library of Work and Play: Needlecraft |Effie Archer Archer
After the satin-stitch has been done, a little back-stitch is worked through the centre of the heavily padded sections.

The Library of Work and Play: Needlecraft |Effie Archer Archer
A good effect is obtained by working one letter in satin-stitch and the other in seeding.

The Library of Work and Play: Needlecraft |Effie Archer Archer

But why apply the term "satin-stitch" exclusively to parallel lines of stitches all of a length?

Art in Needlework |Lewis F. Day

satin stitch

an embroidery stitch consisting of rows of flat stitches placed close together

C17: so called from the satin-like appearance of embroidery using this stitch