There is no "Roman" Catholic Church: Roman is an epithet first commonly used in England after the protestant revolt to describe the Catholic Church. It is rarely used by the Catholic Church. The Chaldean Catholic Church is part of the Catholic Church.

The Chaldean Catholic Church, based in Iraq, of course, and the Syro-Malabar Catholic Church, based in India.

The pope in Rome is the leader of the entire Catholic Church.

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.