The key phrase is - in the round. When you knit on dpns or circs, you’re not going back and forth like straight needles. So to get garter stitch you have to knit one round and purl the next.
Knitting in the round is different from knitting flat because the same side of the fabric is always facing you. If you knit every stitch, you’ll get stockinette. To get garter stitch, you must knit one round, purl the next and so on. Put a marker at the beginning of the round so you’ll know when to switch from knit to purl or vice versa.
No, to do stockinette stitch you don’t alternate knit and purl stitches, as in:
kpkpkpkp.
You alternate ROWS or ROUNDS of knit and purl stitches, as in:
kkkkkkkk
pppppppp
kkkkkkkk
pppppppp
That’s when you knit flat. When you knit in the round, you just kkkkk every stitch and the stockinette pattern emerges automatically.