Monero uses ring signatures and several other mechanisms to separate a transaction from the sender, recipient, and contents so that you can't reconstruct chains of transactions but you can still verify consistency across the blocks. Monero is reasonably private but it's still technically possible to rebuild some fragments of transaction chains even if it's extremely unlikely.

ZCash on the other hand uses Zero Knowledge Proofs to verify correctness of the blocks and the transactions without leaking information about the system (such as the sender, recipient, or amounts). ZCash is much more computationally expensive, needs to be carefully callibrated, and needs the founding keys to be safely destroyed following the bootstrap of the system to remain secure however it does provide stronger and more easily mathematically verifiable assurances of privacy. "The Ceremony" is a really good one-off podcast about the story.

But in general it is possible to have privacy preserving functionality in decentralised services, it just requires far more complicated maths and lots of statistics to make work correctly.