My understanding: Assumption and assignment of contract is basically taking over someone's existing contract. In the timeshare world, this is likely non-deeded property. That doesn't necessarily mean it has an expiration date... just that it's not (or perhaps not yet) deeded property.
My experience: About 12 years ago, we wanted to change the names on a contract purchased a couple years earlier from Wyndham (that still had a loan balance). The deed had not yet been recorded so they had us sign and notarize an Assignment and Assumption agreement. After the loan was paid in full the deed was recorded.
I believe Wyndham also requires an Assignment and Assumption agreement for Club Wyndham Access contracts.