Full disclosure: I have no experience with B31.8.
I just checked, both codes give different values. Close, but different.
I used an example of an expansion of Carbon Steel from 70°F to 200°F. Calculating the expansion manually using table C-3 of B31.3 got me 0.000829in/in. Using Table 832.2-1 of B31.8 got me 0.000854in/in. Those numbers match the ones calculated by CAESAR.
In fact, in B31.3, if you calculate the expansion manually using table C-1, you'd get a slightly different value than using table C-3.