Full Idea
To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency.
Gist of Idea
A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised
Source
GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
Book Reference
Hughes,G./Cresswell,M.: 'An Introduction to Modal Logic' [Methuen 1972], p.19
A Reaction
[They go on to say that Propositional Logic is strongly complete, but Modal Logic is not]