A contradiction is something that purports to be a and not-a at the same time in the same sense. The law of noncontradiction is fundamental to reasoning and logic. This law states that nothing asserting both of these things at the same time and in the same sense is true. For instance, if I said to you “I’m on my way to the store right now,” then turned to your friend with you and said “I am not on my way to the store right now,” then I have uttered a contradiction.
Contraries are statements which both cannot be true in the same time and the same sense, yet could possibly both be false. An easy example is this: “Mary got an A on her test,” and “Mary got a D on her test.” While both cannot be true these are not contradictory. It could be that Mary got a C on her test, and thus both options are false.