Please describe to me the difference between tooth decay, sensitive teeth and sinus pain?

Pain is pain. Tooth decay creates tooth sensitivity, sinus pain can simulate tooth pain because of the pressure placed on the main nerve that runs in the floor of the sinus cavity. Sinus pressure, creates sinus pain, which can often be mistaken for tooth pain. Tooth pain, in the upper arch, can be from sinus pressure, or from tooth decay. Your dentist can be a big help in trying to identify the source of pain.
Difference. Tooth decay - bacteria has penetrated the tooth and eaten away tooth structurre. Sensitive teeth - may be from the gum tissue pulling away from the root and allowing the root to feel the cold water, air, food, etc. Sinus pain - when you have a head cold or you have an infection in the sinus (could be from the root of the tooth next to the sinus) the sinus may hurt until treatment.
Source of pain. Tooth decay, sensitive teeth, and sinus pain may feel very similar. Decay and sensitive teeth cause pain when the tooth's nerve is stimulated. It starts as sharp pain lasting a few seconds, but can progress to something much worse if the nerve deteriorates. Any tooth can have this. Maxillary sinuses are directly above the upper molars, pain from sinus infection will be limited to these teeth.