The second time around shower was originally designed for moms who were having a baby that was not their first. The idea behind this type of baby shower is that every baby deserves a party. Though the goal here is not to necessarily help stock the nursery for the new parents, but merely help them celebrate.
Second time around can refer to the mother or it can refer to the gift. Sometimes it is specified in the baby shower invitation, which can help clear up any miscommunications. If the second time around refers to the gift, be sure to list your criteria. So you might say: “Bring a gently used baby item to share with Mary’s new baby.” Or “When you’re making a favorite dinner this week, prepare a second serving and bring it ready to be frozen in Mary’s freezer to help her out after the baby is born.” If you don’t care what the gifts are, simply leave that information blank.
Everything else would look as much like a baby shower as the mother-to-be and hostess would like it to be.