There are different kind of CPU techologies on todays computer world:

Single CPU Computers are:
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Single CPU computers that have 1 single CPU.
Dual Core computers that have 1 single CPU but with 2 cores in it hence performing like a double cpu computer.
Quad Core computers that have 1 single CPUs but 4 cores in it hence performing like four cpu computers.

Multiple CPU Computers are:
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Dual CPU computers that have 2 seperate CPUS on the same machine.
Quad CPU Computers that have 4 seperate CPUS on the same machine.

After this brief explaination, here is how the technology is shaped:

Dual Core is actually the name of a technology which refers a CPU (Central Processing Unit)'s built in a special way so that it is a single chip that consists of two cores in it. They are basically two co-processors in a single chip and sold as a single unit which is plugged into a single CPU slot. But even though dual core cpus are a single unit, it performs like a double processor since it has 2 cores (2 co-processors) inside.

Dual Core is not a name of a special brand or chip, it is a name of a chip technology. So different brands (Intel, AMD) can have their own dual core processors.

Core Duo is just INTEL's brand of dual core technology. It is a registered trademark of Intel which describes the first revision of its DUAL CORE processors. After Core Duo, Intel also released Core 2 Duo brand which is a more advanced and faster dual core chip structure.

AMD has also its own brand (Athlon 2x) for dual core techology.

"Pentium D" is again a dual core chip of Intel but it is older than Core Duo brand so Core Duo and Core 2Duo's performance are known to be better than Pentium D class computers.