x86 is the CPU architecture that defines all CPUs derived from the Intel 8086, which was Intels first commercially available 16-bit CPU. All PC based CPUs to this day are derived from this CPU, just with a ton of features added on top. The most notable are x86-32 (usually just shortened to X86 as 16-bit OS's have gone the way of the dodo) and x86-64/x64/AMD64, the 64-bit extension to the architecture that AMD introduced in its Athlon 64 lineup that Intel eventually adopted after it's own 64-bit solution (an entirely new CPU architecture, the Itanium) failed in the marketplace.
Anyway, to answer the OP, to move from 32-bit to 64-bit requires re-installing the OS, as the fundamental architectures are completely different.