Welcome to the Forum.
One has to take a bit for granted in your initial post. Not knowing the voltage/phase charistic of the motor we can only assume your 50 amps is correct. Likewise, the type conductor would dictate if #8 was good for 50 amps (ie: NM is not). The 50/70 numbers don't seem to match NEC.
In general, a 40 amp motor would require a 50 amp wire (40 x 1.25), but would allow a 100 amp breaker (40 x 2.5).
But, as Jack33 states, the conductor, sized per 430.21 is considered to be protected by the motor overcurrent device. The breaker serves as short circuit/ground fault protection and is sized per 430.51. The breaker will quite often be twice the conductor ampacity.