Why do we use different indicators for strong acid-weak base titration and strong acid-strong base titration?
Because the end-points of these titrations have different pH values. A strong acid / strong base titration has an endpoint of pH 7, and an indicator that changes near 7 is useful. Phenolphthalein changes around pH 8.5 which is close enough for government work (so to speak). A strong acid – weak base titration will have an endpoint below 7, and so an indicator that changes over a range that is less than 7 should be used. Methyl orange changes around pH 4.