Nope. x86 is a family of instruction set architectures. It can mean 16-bit, 32-bit or 64-bit mode of execution. The 64-bit extension (x86-64/x86_64/amd64) to the x86 architecture is just that: an extension.
Widening the registers and providing opcodes to access the wide registers.
You could also use 128, 256 or 512 bit registers if supported by various additional processor extensions.
If it was 32-bit only, then it’d probably be called x32.

Eric Heitz's Research Page
Real-Time Polygonal-Light Shading with Linearly Transformed Cosines Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt ACM SIGGRAPH 2016 Motivation Shading with area lights adds a great dea…