You're to be forgiven for your confusion, as Intel's marketing arm hasn't made the distinction very clear - not very clear at all, in fact.
Y'see, when talking Core 2 Duo versus Centrino, you're actually talking apples versus oranges. Intel's Core 2 Duo is a microprocessor, the brains of a computer, be it a Windows box or a Mac. It's an actual chip, a piece of hardware. Centrino, on the other hand, isn't a "thing" at all, but Intel's way of wrapping its whole mobile-computing offering - a microprocessor and its supporting chips - into one unified "marketing message."
You'll see microprocessors referred to in some marketing materials (and sloppy technical witing) as "Centrino proccessors," but what that means is that they're processors intended to be used in a Centrino platform - that is, in a mobile system for which Intel will bundle a microprocessor such as the Core 2 Duo with a number of other supporting chips. Among these supporting chips are what are called the northbridge and the southbridge, which control access to other parts of the computer such as memory, hard drives, and the like, and other chips such as those that provide Wi-Fi capabilities. There's no microprocessor named a Centrino.
