The Church of England from which all our churches descend is also called the Anglican Church. But when our country was founded, things English were not that popular (following a war for independence). The same is true of some other countries in the world which have our churches but where relations with the government of England were not that good. As a result, we chose a kind of synonym for the name of the church here--Protestant Episcopal (meaning the church with bishops but not the Roman Catholic one).
Nevertheless, the church has a number of associations and memberships in which the term "Anglican" is used, if not as part of the official church name, and the Episcopal Church, as it's usually called now, is part of the worldwide "Anglican Communion" with the Church of England.
One exception to this, in case it has come up, is that 500 or so American parishes left the Episcopal Church in recent years, thinking that it had become too liberal on a number of matters. Needing to differentiate themselves from the Episcopal Church, they generally have chosen to call themselves "Anglican," referring to the older or original term of this branch of Christianity.
In both cases, some of us lean somewhat more towards things Protestant, while some lean towards things more Catholic. Many people think we are both, in a way.
BTW, I see that you have the Presbyterian Church logo, so you might consider this problem of Episcopal vs. Anglican to be something like the words Presbyterian and Reformed. Yes, there is a difference but not total...and outsiders usually get confused over them.