x86 is the name of the architecture that it’s built to run on (the name comes from a series of old Intel processors, the names of which all ended in 86, The first of which was the 8086). Although x86 was originally a 16-bit architecture, the version in use today is the 32-bit extension.
x64 is actually more correctly “x86-64”–the 64-bit extension of x86. It was developed by AMD under a license from Intel, which may account for the difference in nomenclature (that and the fact that both architectures have seen simultaneous use for a long time, so marking the distinction is important). All things considered, though, it’s easier to just say x64, though, so we stuck with that.