Contrary vs contradictory

In philosophical logic there is a difference between contrary and contradictory statements.

Contradictory

Two statements are contradictory when one must be true and the other must be false. Take these two statements:

The cat is white.
The cat is black.

These are contradictory because they cannot both be true at the same time.

Contrary

Contrary statements are similar to contradictory ones, in that both statements cannot be true at the same time. The difference is that they might both be false. The statements about the cat cannot both be true at the same time – but if the cat is ginger, then neither is true. In that case the statements are contrary rather than contradictory.