Bjarney is correct, but I don't think he answered the question. "Is it 208 amps per phase or is it 208 split across the 3 phases for 69-70 amps per phase?" It is 208 amps per leg, maximum.
It is the same as a 200 amp three phase breaker. Each leg is capable of delivering 200amps, not 200amp divided by 3.
He correctly told you about the voltage issue, where the 208vac is phase to phase voltage, while the 120vac is one phase to neutral. The nameplate shows the two voltages, that is, 120/208 vac, and should also state that this is a 3-phase system.
I am a little concerned that you do not know the difference. Are you really qualified to be using test instruments on live voltages? If not, but have a desire, thats fine, but be careful! One slip could cost you your life.