My understanding of them is that they are both anti-torpedo countermeasures, however what differs is which torpedo mode they spoof.
You are correct that Passive is a noisemaker, however it is designed to be more noisy than your sub, therefore attracting a passively homing torpedo to it in preference over the submarine.
Active is designed to emit a thick cloud of bubbles that to active sonar appear to be a solid object, therefore confusing any torpedo using active homing.
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