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No, that's what a zero knowledge proof is; at the end of the protocol, you are convinced that some statement is either true or false, and learn nothing else about the "proof".

In NP-terms, you learn whether the NP instance is true (eg a 3SAT clause is satisfiable), but learn nothing about the witness (eg the assignment to the clause's variables).

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So, which statement is right/better?

Not completely clear to me what you mean by "calculated to be true", but you may want to look at the difference between computational and statistical zero knowledge. A computational ZK proof hides the witness from computationally bounded (i.e. probabilistic polynomial time) adversaries. Statistical ZK, on the other hand, hides the witness from any adversary, even if they can carry out an unbounded amount of computations (there are slight subtleties there depending on the precise security model but that's the basic idea).

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