Pad stitching is used for attaching the layers of interfacing to the under (or inner) collar or in lapels. It is used for stiffening and shaping. A helpful booklet to have for information on tailoring stitches is "The Workman's Guide to Tailoring Stitches and Techniques". I still have not gotten the stitch down to what one would call beautiful but I am trying. With a chalk pencil draw paralell lines 1/2" apart vertically in the stand section of the collar. There is supposed to be only a thread picked up on the under collar fabric. My stitches are a little bigger than that, still trying to be better. No one will see them because the fall part of the collar will cover them.
For this particular frock coat I have used some navy wool flannel for the under collar that matched my outer fabric in color fairly well. The outer part of the collar is then attached to the inner with a "prickstitch" which is hand done. You could use a sewing machine but I have found that doing it by hand makes a nice edge and tends to keep the under collar from peaking out.