How can i tell the difference between a pulled muscle and a slipped disc in my back lower right side of my back. hurts to move in certain ways

You : You cannot. If yo have a pinched nerve from a disc herniation you may have weakness to your legs or may experience numbness, tingling or abnormal sensations to the legs. That would not be seen with a "pulled muscle".

Back: While both can cause pain in your back slipped discs very commonly also cause nerve pinch type symptoms with pain radiating down the leg. Ultimately, an evaluation from your doctor and perhaps an MRI would be helpful.