The term for referencing a line of rulers from the same family is dependent on whether the line itself or the period of time in which the family ruled is being referenced. A monarchy is a line of rulers in which lineage determines the successor to the throne. A dynasty is a period in history in which a particular family rules a kingdom.
Dynasties are not always universally classified. Some historians divide periods of history differently. In general, though, dynasties follow the period during which a particular family, or branch of a family, rules until another family, or branch of the existing family, takes over. Sometimes, dynasties lost control of their lands simply because the entire family eventually died, leaving no heirs to assume power. Egypt and China were ruled by dynasties during their early histories. In the United States, the term dynasty is sometimes applied to powerful groups or entities that maintain control of an institution for a long period of time. Sports teams are sometimes referred to as dynasties for this reason. In this case, unlike the historical definition, the term is applied as a reference to the organization's strength and not to imply any familial bonds or connections.