in US residential typically has 240v split-phase service, split to 2x opposite phases 120v (hots) in home distribution panel, and a neutral usually tied to local ground at house. You have 2x clamps only to read the separate currents in the hot lines, not voltage (you are not completing a voltage reading circuit with the clamps). If you accidentally clamped one on neutral then that current would read 0 or close to it. But the hot clamp would read Something, if working at all.
if you accidentally clamped both onto the same line, with the clamp directions reversed, then you could conceivably read 0 all the time. But even in that case, I’d expect to see some small amps/wattage difference between the clamps in different readings, due to the small manufacturing differences in the clamps and phase of the moon.