Calculus or tartar is a form of hardened dental plaque. Brushing and flossing can remove and prevent calculus from forming, but once formed it has to be removed by a dentist. A manual or an ultrasound instrument is used during this procedure.
A cavity, dental caries, is an infection caused by bacteria (streptococcus mutans) that causes demineralization and destruction of the hard tissues of the tooth. During a dental restoration, the dentist drills away the infected part of the tooth and then fills it with a isolating filling. If the tooth continues to ache, a rooth canal treatment might be in order.
An aching or strongly scurrying tooth can be a sign of that the root canal pulp could be infected, and in that case a root canal treatment would be in order. During a root canal treatment the root canal pulp is removed, the canal is cleaned and the tooth sealed, which prevents more bacteria from penetrating the tooth. If the tooth still continues to ache, the tooth might have to be extracted.