Victorians are people who lived during Victoria's reign (1837-1901), and their successors were Edwardians.
The current British queen is Elizabeth II, but "Elizabethan" refers strictly to the reign of Elizabeth I.
Why is it that Britons of the 21st century and the second half of the 20th century are not Elizabethans? It can't be that the proper adjective is only allowed to apply to the first monarch of that name, because the Edwardians lived during the reign of Edward VII, and the Georgian era covered the reigns of Georges I to IV. Is it simply to do with the period being historically significant enough to be named after the monarch of the day?
Generally those names are given to periods of time for their distinctive cultural identity and historical importance.
Elizabethan England was notable for being the time of Shakespeare, the foundation of England's first colonies, and the return to a stable monarchy after the Wars of the Roses and the succession issues of Henry VIII. Georgian England denotes the time when Great Britain was ruled by monarchs of German descent who were also the Electors of Hanover, and saw the development of Parliament as a more independent organ of government, as well as the conflicts in the American colonies (e.g. The Seven Year's War, the American Revolutionary War). The Victorian Era usually refers to the latter part of the reign of Queen Victoria, which was notable for imperial expansion, industrialization, and is associated with a specific culture and dress (reserved and "proper," one might say).
In short - those are names to describe periods notable for unique circumstances and a specific culture. I'd rather not comment on whether or not the reign of Elizabeth II might be referred to as another "Elizabethan Era" out of fear of violating the 20-year Rule.