The answer is: yes. There are general guidelines for matching sleeping positions to pillow types, but they are not hard and fast rules. Why? Because almost all of us switch positions throughout the night. You may be a side sleeper and also spend some time on your back at night. The same goes for the stomach croucher who occasionally moves to one side. You want a pillow that fits all your sleeping positions.
That said, here are some broad guidelines:
Side sleepers may need a firmer pillow and a thicker pillow. Look for one that is as thick as the distance between your ear and your outer shoulder.
Stomach sleepers may need a soft pillow -- or no pillow at all -- under their heads. Placing a pillow under your stomach and pelvis may help prevent back pain.
People with backrests may need a flatter pillow to keep the head and neck aligned. People who sleep on their backs may want a softer pillow -- but if you have neck pain and sleep on your back, look for one that provides extra support while maintaining a softness that's comfortable for you.