There's two major widths in a processor. The data register width and the address bus width, but even that is not the whole story. If you go back to a processor like the 68000, the classic 16-bit processor, it has:
32-bit data registers
16- bit ALU
16-bit data bus
32-bit address registers
24-bit address bus
Some people called it a 16/32 bit processor, but really it was the 16-bit ALU that classified it as 16-bits.
If you look at a Zen 4 core it has:
64-bit data registers
512-bit AVX data registers
6 x 64-bit integer ALUs
4 x 256-bit AVX ALUs
2 x 128-bit data bus to DDR5 (dual edge 64-bit)
~40-bits of addressable physical RAM
So, what do you want to call this processor?
64-bit (integer width), 128-bit (physical data bus width), 256-bit (widest ALU) or 512-bit (widest register width)? Do you want to multiply those numbers up by the number of ALUs in a core? ...by the number of cores on a piece of silicon?
Me, I'd say Zen4 was a 256-bit core, but you could argue any of the above numbers.
Basically, it's a measurement that lost all meaning so people stopped using it.