I don’t blame you for being confused. I’m Anglican, and I’m confused by it all.
Anglicanism has gone through a lot of different phases. I suppose one could say that the first phase was under Henry VIII, in which it was a rather strange hybrid of Catholic practice and belief with innovations such as the rejection of all forms of papal authority, the destruction of monasticism, the pruning or outright rejection of devotion to the saints, etc. Meanwhile, Protestant teaching gained ground, and after Henry’s death England became Protestant outright. At this point, for six years, it definitely was just part of the broader Reformation movement. Important continental theologians came to England to teach, and so on. Then under Mary, England was reconciled with Rome.
Then in 1558, Elizabeth I came to the throne. She reestablished the Protestant Prayer Book and a revised version of the Protestant Articles of Religion, and she was duly excommunicated by the Pope. Under her, England was clearly Protestant–it was doctrinally part of the broader Reformed movement, as distinct from Lutheranism (at this point, Anglicans saw themselves as more Protestant than the Lutherans, something that would shock many Anglicans today). But we kept the hierarchy and our liturgy retained many Catholic elements. The more radical wing of Anglicanism (the “Puritans”) wanted further reforms that would have brought us in line with Calvinism in the strict sense (the doctrine and practice of Geneva). We rejected those reforms.
Instead, in the 17th century, we began moving back toward a more Catholic position, reinstituting some ritual that had been discarded, distancing ourselves to some extent from Calvinist views of predestination (at least many of our theologians did this–others did not and some are Calvinists today), and deepening our appreciation of the Fathers and of Christian tradition generally. There were some other swings back and forth, but by the early 19th century Anglicanism was still decidedly Protestant, but was definitely the most Catholic expression of Protestantism and contained a “high church” wing that saw itself as faithful to the teaching of the undivided Church before the East-West schism.
Then, in the 19th century, the Oxford Movement began. These guys claimed to be restoring the truly Catholic identity of Anglicanism. The idea was that while we had been infected with Protestantism, our basic doctrine and practice had remained Catholic, and we were the “third branch” of the Church along with “Rome” and the Eastern Church. There was a lot of nostalgia and historical fudging in this view, but it had a huge effect on our doctrine, and even more on our worship. It created an “Anglo-Catholic” wing of Anglicanism who genuinely saw themselves as Catholic (though not “Roman Catholic”) rather than Protestant–while all the while other Anglicans remained staunchly Protestant, and the great mushy middle absorbed the idea that we were some kind of “middle way” between the two. Hence the situation you have observed.
Think of us as a very broad tent ranging from “Catholicism without the Pope” (and with better liturgy) all the way over to a moderate Protestantism, which has Calvinist, charismatic, and liberal branches. What we have in common (absent some of our blatantly heretical bishops whom we notoriously fail to discipline) is a commitment to the Nicene Creed, some form of the historic Prayer Book liturgy (now revised in increasingly radical ways so that it may no longer function as a unifying factor any more) and to a vaguely defined consensus of early Christian tradition.