bigamy-the crime of marrying a person while already legally married to someone else polygamy-the fact or custom of being married to more than one person at the same time
Does bigamy refer to the re-marriage itself and polygamy doesn't?
I think the biggest difference is that in bigamy the wives are not aware that the man has other wives (and all the wives live in different places), while in polygamy the wives know all the other wives (and all the wives live in the same place).