8/16/32 Bits of microcontrollers
The "bit size" of a CPU typically refers to the size of its general-purpose registers (or its primary register, in parts with nonuniform registers). For example, the MC68000 is generally considered a 32-bit architecture as its registers are all 32 bits wide -- even though it has a 16-bit data bus and a 20-bit address bus. (This means that it must make two memory accesses to write a single register to memory. The top 4 bits of an address register are simply ignored, which is a bit of an oddity.)

The sizes of the address and/or data busses connecting the processor to its various memories are often different, either from the size of registers or even from each other. In more complex architectures, it is not uncommon for the same memory to even be accessible over multiple data busses of different widths.