The differences between the sizes
Everything we have done so far is applicable to 64-bit as well as 32-bit; the only thing you would need to change is switch out the p32() for p64() as the memory addresses are longer.
The real difference between the two, however, is the way you pass parameters to functions (which we'll be looking at much closer soon); in 32-bit, all parameters are pushed to the stack before the function is called. In 64-bit, however, the first 6 are stored in the registers RDI, RSI, RDX, RCX, R8 and R9 respectively as per the calling convention. Note that different Operating Systems also have different calling conventions.