I'm learning about how processors send an address to ram through the address bus, and receive and send data from ram through the data bus. In the videos I have watched, the processor was an 8 bit processor that had 8 wires coming out for the data bus, and 8 wires coming out for the address bus, where each wire carried one bit of information, either off or on. That got me wondering. Does a 32 bit processor basically work the same way, but it can send more bits through the address/data bus at one time. What about a 64 bit processor. I haven't learned about registers yet, but I'm getting there. Does it have something to do with the size of the registry? I understand the parts of a processor, but I don't understand what people mean when they classify a processor by its bit capacity.
There are several components in a microprocessor that may all have their individual size: data bus, address bus, registers, and ALU (arithmetic logic unit). Modern CPUs also have caches, memory management units, floating point and single instruction multiple data (SIMD) units. (Also nowadays you have multiple CPU cores in one CPU.)
All those units may have their own bit size. E.g. the 68000 had a 16 bit data bus, 24 bit address bus, 32 bit registers and a 16 bit ALU (and none of the modern stuff).
Historically, the processor classification in bits (8, 16, 32, 64 and so on) gives the size of the ALU. This means that an 8 bit processor can handle 8 bit of data in one cycle, a 16 bit processor 16 bit data and so on. This does not mean that they can't handle larger data, it just takes longer. E.g. the 68000 required two cycles to add two 32 bit values.
A 64 bit processor has a datapath and memory address width of 64 bit. The integer size is also 64 bits. In addition the registers, address bus and data bus is 64 bits wide.
Likewise in a 32 bit processor the datapath, memory address width, integer size, register size, etc are 32 bits wide.