A ZKP allows a “prover” to prove to a “verifier” that a given statement based on the prover’s data is true without conveying any information apart from the fact that the statement is indeed true. This is extremely useful in the context of blockchain technology (as evidenced by protocols such as Zcash and Mina).
However, NMC is not blockchain technology. Consequently, while ZKP relates to proofs of the state of data that one party has in their possession, NMC delivers rich, privacy-preserving computational capabilities for data that any number of parties can hold.
Source: Whitepaper page 9