A regnal year is a year of the reign of a sovereign. From Latin regnum meaning kingdom, rule.
The oldest dating systems were in regnal years, and considered the date as an ordinal, not a cardinal number. For example, a monarch could have a first year of rule, a second year of rule, a third, and so on, but a zero year of rule would be nonsense. Applying this ancient epoch system to modern calculations of time, which include zero, is what led to the debate over when the third millennium began.
An era name was assigned as the name of each year by the leader (emperor or king) of the East Asian countries of China, Korea, Japan, and Vietnam during some portion of their history. The people of the country referred to that year by that name. Era names were used for over two millennia by Chinese emperors and are still used by Japanese emperors. It could last from one year to the length of the leader's reign. If it lasted more than one year, numbers were appended to the era name. If it lasted the entire length of the leader's reign, then that leader is often referred to by that name posthumously. However, the leader was often given a more complex formal posthumous name as well. It should not be confused with a temple name, by which many leaders are known. The Republic of China era can be construed to be an era name, albeit one without an emperor.
In England, and later the United Kingdom, until 1963, each Act of Parliament was defined by its serial number within the regnal year in which it was enacted. Each regnal year begins on the anniversary of the day the sovereign succeeded to the throne. A table of English regnal years, from 1066 to 1962, is given here