In current terminology
x86 normally indicates 32-bits, with
x64 indicating 64-bits.
x86 really refers to an instruction set based on the Intel 8086 (from some time ago - 1973 by Wikipedia's reckoning). Nowadays this normally is taken to simply mean a 32-bit instruction set. Initally it was a set of instructions that operated with only 16-bit, so historically could be referred to as
x86-32. But, obviously,
x86-16 is no longer relevant as 16-bit processors died out a long time ago.
x86-64 (or just
x64) is an extension to the
x86 instruction set, providing support for 64-bit registers, memory space and the like. It is fully backwards compatible with the 32-bit
x86 instruction set (allowing 32-bit software to be compatabile without modification in most cases) and is taken to simply mean a 64-bit instruction set.
There are vendor-specific names for
x86-64 as well - it can be referred to
Intel 64 (previous