The microprocessor package for a Core 2 Duo microprocessor contains only a single chip containing two cores and accompanying cache.
The microprocessor package for a Core 2 Quad microprocessor contains two chips each containing two cores and accompanying cache. The two chips are connected to a multi-chip-module. There is little logical difference between a Core 2 Quad in a single socket, and a pair of Core 2 Duos in two sockets.
Starting with the Nehalem series of microprocessors all of the cores were integrated into a single chip. Some variants of the Westmere microprocessor contained an IGP within the package as well, as a separate chip.
All Sandybridge and Ivybridge microprocessors exist as a single chip with all components integrated including the IGP (where present).
Some variants of the new Haswell microprocessor contain a DRAM cache known as Crystalwell which exists as a separate chip inside the package.
I hope that this answered your question.