The number of basis cases does not determine which inductive method you're using, rather the inductive hypothesis.
With weak induction on a natural number n, we wish to assume that k<n is true for *some* k and show that k+1 is true.
With strong induction on a natural number n, we wish to assume that for any c =< k < n, k+1 is true *for all* k, where c is the value of one of our basis cases, and show that k+1 is true.
The tried-and-true domino allegory works well here. Weak induction ensures that if I pick any one domino to knock over, the next one must fall as well. Strong induction ensures that if I knock down one domino, every single domino afterward must also fall.