Is the Anglican Church the same thing as the Episcopal Church?
Yes and no.
The Anglican Communion is a worldwide fellowship of groups that originated from the Church of England, which separated from the Roman Church in the 16th Century. Many of these branches refer to themselves as the "Anglicvan Church", for example the Anglican Church of Canada and the Anglican Church of South Africa.
At least two of these branches, those in Scotland and the USA, refer to themselves as the "Episcopal Church". That is because the main established church in Scotland was Presbyterian, meaning it did not have bishops. So the Anglican Church in Scotland was called the Episcopal Church to indicate how it differed from the Presbyterians, and that was also taken over by the USA.
Some bodies have also broken away from the Episcopal Church in the USA because of doctrinal disagreements, and some of those call themselves Anglican, for example the Anglican Church of North America. But they are not part of the Anglican Communion as the Episcopal Church of the USA is.