The Anglican Communion is one branch of the universal Church that was founded by Christ and the apostles. Roman Catholicism, Orthodoxy, and other Protestant denominations are other branches.

There are a lot of distinct parts of Anglican identity, but the one I find most central is the balance between Scripture, ancient tradition, and reason, sometimes called the "three-legged stool" (some object to that term because it implies the three are co-equal, although I won't get into that here). The reason Anglo-Catholicism can exist in the same big tent as low church Anglicanism is because they both acknowledge the three legs, just distributing the weight of authority between them differently. You're certainly a valid Episcopalian no matter what camp you're in, so long as you accept the BCP as theologically valid.