If anyone is actually curious.
The x86 is shorthand for 8086 (the original intel processor) and 80286. Many people just called the 80286 the 286. By the 386 I don't think anyone used the 80 prefix anymore. Intel tried (and failed) to trademark the number 86 and as such the 586 was called the pentium instead. All processors based on Intel technology (including AMD) just call it x86. This was all fine and good until AMD said that 32 bits wasn't good enough anymore. AMD invented a 64 bit mode of the x86. They call it AMD x86-64. Intel later invented their own, but it was too late people already used AMD's implementation and didn't want to use Intel's. So intel dropped it and AMD x86-64 became the standard. Later on people just started calling it x64.
So x86 is older 32 bit processors derived from the 8086 and x64 is short for x86-64 based on AMD technology.