Sensitivity in the teeth and sensitivity in the gums are two different situations, with different causes.
In the case of sensitive gums, they are caused by plaque deposits over the teeth, commonly known as bacterial plaque, which is normally eliminated through brushing or flossing.
However, when plaque is not eliminated it tends to harden and forms lumps we know as calculus or tartar. Bacteria cause swelling in the gums (gingivitis), which causes redness, inflammation and often bleeding of the gums.
In the case of tooth sensitivity, pain will also be present when the teeth are in contact with cold food or beverages, or even with cold air. Patients may also suffer discomfort when brushing their teeth.
Tooth sensitivity is different to gum sensitivity in that it is only a temporary pain. Usually, it is caused by wearing of the tooth surface, the enamel, or because of gum recession.