Both a nightguard and a sports mouthguard are meant to protect teeth, but they protect in different ways.
The night guards are used to protect the surface of teeth and protect it from being worn down from continuous grinding and clenching. The main motive to wear a sports mouthguard is to protect the teeth and mouth in case of sudden, hard impact. A night guard is made from durable hard plastic. This will last for a longer period of time against grinding whereas a soft mouthguard is made from a softer material that can take up all the force or unexpected impact. The night guard is used to cover the biting surface of your teeth. A sports mouthguard should cover your teeth including your gums.
It is safe to say that purchasing a store-bought guard is a compromised choice. The best solution is to have a professional nightguard or sports mouthguard made for the optimum protection of your teeth.