There is the Church of England, which has the Archbishop of Canterbury as its senior cleric and the Monarch as its formal head, and there are the many churches in the Anglican Communion which share common ideas and work together but are in no way subject to the Church of England, or to the Archbishop of Canterbury or Monarch. Most of these churches call themselves Anglican, but some Episcopal (as in the USA) to stress that they are not English, or some after the name of the country, or whatever.
There is a good Wiki article which explains the situation much more fully:
Anglican Communion - Wikipedia
There is a good Wiki article which explains the situation much more fully:
Anglican Communion - Wikipedia