The assumption is that they've got everything. It's the reason second babies get fewer presents, and it's about a third true.
What survives from the first baby is the durable equipment. What doesn't is everything soft, everything that was washed twice a week for two years, and everything that was sized for a season that has since passed.
What they've genuinely still got
The furniture. The stroller, probably. The plastic things that don't wear out — bottle racks, bowls, the bath. Nobody needs a second one of those, and buying one is how you end up in a hallway conversation about storage.
What's quietly gone
Anything soft. Blankets, swaddles, hooded towels, muslins. Two years of washing takes them from lovely to serviceable to rag. They're still in the house; they're not still nice.
Sleep sacks in the small sizes. Outgrown, and often passed on or worn out. The newborn and 0–6 month sizes are the ones least likely to have survived.
Bibs and smocks. Stained beyond recovery. Nobody keeps these.
The comfort toy. This one's important — the first child's favourite is emphatically not available for the second. It's spoken for, and any attempt to reassign it will be resisted with feeling.
The timing thing nobody mentions
A second baby often arrives in a different season from the first. The 0–3 month clothes and the newborn sleep sacks are for the wrong weather, and that's not something anyone thinks about until the week it matters.
If you know roughly when the baby's due, buying for the right season is a genuinely useful piece of thinking — and it's the kind of thing only someone paying attention would do.
The gift that lands second time round
Something for the older one.
Not a consolation toy — those are transparent and land badly. Something small and their own, given at the same time. A new sibling is a significant event for a two-year-old and largely a downgrade from where they're sitting.
The other version of this: give the parents something that isn't for the baby at all. Second-time parents are not short of baby items. They're short of time, hands and anything nice for themselves.
If you want the simple answer
Buy the soft things, in the next size up, for the season the baby will actually be in.
It's unglamorous and precisely right, and it's the category they'd otherwise replace themselves in a supermarket at eleven at night.