Full Idea
Under strong Kleene tables, a disjunction will be true if one of the disjuncts is true, regardless of whether or not the other disjunct has a truth-value; under the weak table it is required that the other disjunct also have a value. So for other cases.
Clarification
'Kleene' is (oddly) pronounced 'Claynee'
Gist of Idea
Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value
Source
Kit Fine (Some Puzzles of Ground [2010], n7)
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.116
A Reaction
[see also p.111 of Fine's article] The Kleene tables seem to be the established form of modern three-valued logic, with the third value being indeterminate.