pattern stitches in knitting are named for there final appearance, not for the method used to create them.
so stocking knit is a pattern that is characterized by:
having a fabric that is smooth on one side (with the 'interlocking Vs' and bumby on the other side, showing the passage of the yarn, and the heads of the stitches. each side of the fabric has a very different appearence
Garter stitch is :
a horizontally ridged fabric, with alternateing rows of smooth knit stitches, (the receed) and bumby purl stitches both sides of the fabric have an identical appearance.
When knitting flat (and turning the work at the end of every row), stocking knit is created by working alternate rows of Knits and Purls.
when working in the round, stocking knit is created by knitting every row.
When knitting flat (and turning the work at the end of every row), garter stitches is created by by knitting every row.
when working in the round, stocking knit is created by woking alternate rows of Knits and Purls
there is similar confusion with sead stitch and 1 X 1 ribbing (both patterns consist of "*K1, P1!)
IN KNITTING IT IS THE FINAL APPEARANCE, NOT THE PROCESS THAT DEFINES THE "PATTERN". (this can't be said often enough!)
(and while i don't usually purl every stitch/every row for garter, i too, don't mind purling and have worked patterns backwards and ended up with more rows of purls than knits. )