The ships are identical and the staff shifts between them. However - - -
Magic makes seven day cruises alternating between eastern and western Caribbean. Days at sea followed by true Caribbean or Mexican ports. Since it is for a week, the children's programs, which no other cruise line can come close to matching, really have a chance to gel. The kids are formed into teams, or packs, by age and have a chance to bond with their highly trained, well paid professional counsellors. The atmosphere is much more layed back.
Wonder, on the other hand, does three and four night trips to the Bahamas each week. For the most part, the cruise is part of a seven day Disneyworld/cruise package. Families are bussed aboard after three or four days in the park and have run out of civility and clean clothes. Same programs and the kids have just as good a time, just doesn't last very long. Nassau and private island on the three night cruises, Nassau, private island and alternate Freeport or day at sea on four night trips. No one really settles down. Kids are fine, parents are just short of hysterical. Relaxing it ain't. You can have a good time if you are just doing the cruise and can ignore boneheads.
Magic is a normal seven day cruise with a Disney flavor. Wonder is an extension of the theme park that floats.
With either, you will be up to your ears (no pun intended) in Disney.
More than you ever wanted to know.