A quad core has 4 physical processors on it. A P4 is a single core processor. Most of them have hyper threading with creates a second logical core. The Core 2 Quad series by Intel has two Core 2 Duo chips on it. It's not a true quad core. The Phenom series is a true quad core and so is the i7 series. The i7 also have hyperthreading giving them 8 cores. 4 physical and 4 logical.
The cores also run at different speeds, known as clocks. However, when you have 2+ cores, you do not add them to figure out the total speed. A computer will use multiple cores as it sees fit. Also, a dual-core may not necessarily be slower than a quad-core. Performance varies with clocks, front side bus/hypertransport link, and use.
This is how fast the processor communicates with the memory controller. (North Bridge)
The processor has to go through the north bridge to "talk" to the memory. The i7 series has eliminated this practice for the Intel based line.
AMD has the memory controller embedded on the CPU. They still have a north bridge. But it's between the processor and the graphics card.
The processor has direct connection with the memory.