Full Idea
A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics.
Gist of Idea
'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.8
A Reaction
Similarly, 'weakly complete' is when every logical truth is a theorem.