The Assyrian Church of the East is not in full communion with
the Holy See and the Catholic Church, so the Assyrian Church of the
East is not Catholic at all to begin with. However, some parishes
that were once under the Assyrian Church of the East have since
come into communion with the Chaldean Catholic Church and some of
these Chaldean Catholic parishes kept Assyrian in their name, but
they are still Chaldean Catholics. Chaldean Catholics are of the
Chaldean Rite, which is an Eastern Rite in the Catholic Church, so
they, Chaldean Catholics, are also Eastern Catholics. The only
Assyrian Catholics are those Catholics that are of the Assyrian
ethnic group.