Typically, the lower back pain will be dull and achy with a muscle strain. It may diffuse over both sides of the lower back but mainly stays within the lumbar region.
With a disc issue, you not only have low back pain, but you also can have radiating pain into the buttocks, the hip, or even into the leg or the foot. Discs tend to have more nerve involvement than a pulled muscle or muscle strain. The best thing to do would be to get it examined by a doctor who specializes in determining the underlying cause of the problem.