I am having some confusion between address bus size, physical address size and word size however (I do understand that unit of memory access is word and when word size is one byte then it's known as byte-addressable).
Is address bus size same as physical address size
No, not necessarily. Especially with modern 64 bit address bus sizes, it is quite common that CPUs do not actually support 64 bit physical addresses.
For example, the first AMD64 CPUs had 40 bit physical addresses, the current ones have 48 bit. In fact, due to the Page Table Entry format, physical addresses cannot be larger than 52 bit.
and is that the same as word size?
No, not necessarily. It makes stuff easier, but there have been architectures where the bus was half the word size, and you had to transmit a word in two bus cycles. Conversely, it is also possible to have the bus width be an integer multiple of the word size, making it possible to transmit multiple words per bus cycle.
Just as an example: the IBM 704, one of the most famous computers of all time (both FORTRAN and LISP were first implemented for the IBM 704, the trajectory data for Gemini and Apollo was computed on one) has 36 bit words but 15 bit addresses.