The original Intel Core Duo laptop supported only 32-bit OS. Core 2 Duo supports 64-bit OS, but is usually supplied with 32-bit Windows pre-installed. AMD 64-bit laptops could be running 32-ibt or 64-bit OS.
Intel Dual-Core technologyisa collective term that refers to all Intel dual core processors. Intel Core Duo and Intel Core2 Duo brands refer to specific Intel architectures. The former of these is a 32-bit dual-core technology that first appeared in Intel mobile processor parts. The latter is the 64-bit dual-core technology, also called Intel 64 architecture, as it applies to dual-core processors. That 64-bit architecture is also used in the Intel Core2 Quad processor package, which packs 4 cores into a single package.