Microprocessor architecture bits vs bus sizes
As with many texts written for beginners the situation has been somewhat simplified.

The assumption is that a 32-bit processor does all address operations and calculations also in 32 bits. From that it assumes a 32-bit address bus. Therefore the maximum address range is 4GBytes.
That same reasoning is then extended to a 64-bit processor. 

In real life it can be a lot more complex. A good example would be the MC68000 processor, which was sold as a 16-bit processor, had 32-bit wide registers and a 24 bit address bus.

If a processor has an MMU that can also extend a 32-bit address bus to more bits. There are some 32-bit processor systems out there with a 40-bit address bus.
In the early days of computing I added a sort of MMU* to my MC6809 processor which extended the 16 bit address bus to 20 bits giving me a whopping 1Mbyte address range with an 8-bit processor.

*A 16x8 SRAM.