These refer to essentially the same thing (when it comes to the baby product), although rusk can also be used in BrE to refer to a kind of bready stuff that's added to sausages. Zwieback rhymes with 'lie back' or 'lie Bach' (if Bach has a hard /k/ sound at the end) in my dialect, but American Heritage lists a number of alternative pronunciations. It comes from the German for 'twice baked', as that's what they are: first baked as a loaf, then sliced and baked again. In other words, they're biscotti for babies. (In South Africa, rusks are used just like biscotti--eaten by all ages, dunked into coffee or tea.)
Strangely, we weren't able to buy any of this staple of babyhood in the US, although we searched for it in supermarkets and (AmE) drug stores (=BrE chemist's shop, more or less) in three counties. Sometimes we found the empty space on the shelf where they were supposed to be, sometimes not even that. I searched on the web for signs of a recall or shortage, but found no information, except that, like all finger foods apparently, Gerber zwiebacks now carry stern warnings that they should not be given to children who cannot yet crawl with their stomachs lifted off the ground. They've made them part of their 'Graduates for Toddlers' range, suggested for age 10+ months. But, of course, you need them when the baby is cutting her front teeth, long before toddlerdom. Meanwhile, I just ordered some rusks from my UK on-line grocery and found them label(l)ed 'suitable from 4 months'. (Granted, they do give a recipe for making a sort of porridgy thing from them, so that's probably what's suitable for a 4-month-old.) I have to assume that the warnings on baby foods are the product of the litigious culture...but the warnings are so uniform across the brands/products that I wonder whether they're legally required. (Do any of you know?)
Though we didn't find zwiebacks, we did find some non-zwieback teething biscuits (and ignored age and crawling requirements), which Grover loves (and handles very well, despite being completely uninterested in crawling, since crying for Mum/Mom and Dad to pick her up and carry her wherever she wants to go has worked so well for her thus far). This made me return to thinking about biscuits. As we've discussed before, BrE biscuit is and isn't equivalent to AmE cookie, but in discussions comparing those two words, we tend to only mention the AmE sense of biscuit that refers to a scone-like (in appearance, at least) thing. We should acknowledge areas of overlap with BrE biscuit. Americans do use biscuit in the names for some cookie-like things: teething biscuits and dog biscuits. In both cases, these kind of biscuits are hard--harder than normal (BrE) biscuits/(AmE) cookies. I wonder whether these AmE uses of biscuit remain closer to its etymological meaning 'twice cooked', since teething biscuits (at least) typically are twice-baked (perhaps dog biscuits used to be twice-baked, too?). But note that in both of these cases, biscuit in AmE is used as part of a compound. We don't use biscuit alone to refer to crunchy things like these.
Pressing deadlines mean that I have to reduce my posting even further, I'm afraid. I have told myself that I can only blog once a week now, though it pains me to type that. I promise to work on that backlog of requests from kind readers.