Garter stitch will always look like garter stitch no matter what size your needle is. You will only get stitches that look like stockinette stitch if your doing that stitch.
Garter is knit every row (or purl every row)
Stockinette stitch: Row 1 (rs): Knit every stitch
Row 2 (ws): Purl every stitch
Repeat those 2 rows