Soundness Soundness and consistencyconsistency are properties of deductive systems. Soundness can only be defined with respect to some semantics that is assumed to be given independently from the deductive system.
In the realm of semantics the two properties are related
Definition 1(Soundness[Semantics] -- borrowed from Wikipedia) Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based.
Definition 2(Consistency[Semantics]) A set of sentences $A$ in the language $\mathfrak{L}$ is consistent if and only if there exist a structure of the language $\mathfrak{L}$ that satisfies all sentences in $A$. A deductive system is consistent if there exist a structure that satisfies all formulas provable in it.
ItWith the two definitions given above it is clear that soundness implies consistency. I.e. if the set of all provable sentences holds in all structures of the language then there exists at least one structure that satisfies them.