Three words, three trust models. One of them means handing your coins to a stranger.
These get used interchangeably and they should not be, because the difference is precisely the thing you are choosing between.
You send coins to an operator. They hold them, mix them with other people's, and send different coins back. It works until it does not: they have your funds and can keep them, and they know exactly which output belongs to which input. Every exit scam in this category worked identically, and nothing in the design prevents the next one.
The same, with better hygiene — several addresses, delays, split payouts. The custody problem is untouched. If someone must hold your coins to mix them, they can decline to return them, and they can always tell which is which.
No shuffling by hand and no custody. You deposit into a program whose only way to release funds is to whoever presents a valid zero-knowledge proof. Withdrawing proves you own one of the deposits without saying which. The operator cannot pay themselves your deposit because no code path exists to do it, and cannot pick your withdrawal out because the proof does not carry that information.
This is the third kind. The mechanism, in detail.
Taking away the operator's power to steal also takes away their power to help. No password reset, no support queue. The note is the only key, it lives only in your browser, and if it is lost the deposit stays in the pool permanently. That is not a policy anyone could be talked into changing — there is no instruction in the program that could act on the decision.