In television credits, what's the difference between "producer" and "produced by"?

I was watching the second season of the Cosby Show on Netflix, and I
noticed that the opening credits indicated that the show was "produced
by" Caryn Sneider, but that the "producer" was Carmen Finestra. I've
also seen other shows with credits indicating that they were "produced
by" a different person from the "producer." What gives?