They're expecting a living Santa Claus who looks nothing like St. Nicholas to come and give them rewards for their good behavior.
The Santa Claus still being alive is usually explainedin two types of ways:
1. "He's immortal!" The oldest stories of a Santa Claus of the sprt that doesn't resemble the historical St. Nicholas describle him as AN ELF.
2. "He passes the tradition along generation to generation to the next Santa Claus." In other words, Santa is the Phantom. Or Shamu.
This is the basic plot of everything from the The Santa Clause movies to Sonic Christmas Blast (and most of it is made by Disney, which has always strived to sell Paganism and Witchcraft to children, and wouldn't know Christianity if Donald Duck smacked them upside the head with a Bible).