what does x32 and x64 mean in regard of what bus?

It's the size of the internal registers in the CPU; how much data can be operated on / read / stored etc. in a single instruction.

It does not necessarily apply to either (external) bus.

(I've never designed an i86 type system so I'm now referring to various generic CPUs, rather than specifically current PC types).

Many CPUs have large register sizes and (usually) internal cache, but smaller external address and data buses to reduce system costs - they use two or more successive memory transfers to do a 'wide' transfer over a narrower data bus.

There are 16 bit & 32 CPUs that only have an 8 bit data bus, and 32 bit with a 16 bit data bus.

Probably also 64 bit with 16 or 32 bit buses.

Many do not use the entire (internal) address bus on external pins - they could address far more than would ever be used in any practical design so leaving some out makes the device cheaper; eg. some used 24 bits out of an internal 32 bit address bus.

With PCs, due to the complex internal caching and memory management systems, many CPUs now have two or more times the external data bus width than the internal CPU data bus - it allows different memory modules to be accessed simultaneously.

[Electronics designer & programmer for 40 years].

It corresponds to the data bus width. This usually, but not necessarily corresponds to the register width too.

It could correspond to the address bus width but there is no point in having more address lines than the maximum RAM than can be physically connected. So with a 64 bit CPU, there's little point in providing more than say 40 address lines.