There are also many independent Catholic churches, which fall under the Utrecht line of succession from the Old Catholic tradition.
I’m an Anglo-Catholic who also has an interest in the Liberal Catholic tradition, which is an Old Catholic-type body that emphasizes liberal theology, freedom of conscience, universalism, esotericism, and the unity of all religions/theosophy, things which I all believe in. I chose to formally affiliate as an Anglo-Catholic because I wanted the benefits of affiliation with a major recognized Christian denomination (the Episcopal Church) rather than be a dissident in the Roman Catholic church or be affiliated with an independent church, which are generally not so firmly or formally established, and have a transient, fly by night structure, with no accountability or recognition. I do sympathize with folks in these churches, such as the ANCC, Ecumenical Catholic Communion, etc. with which I share the same attitudes on social and political matters in the church, such as who gets to be admitted to the sacrament of Holy Orders, divorce/remarriage, contraception and abortion. egalitarianism, etc., but I’d rather be affiliated with the larger body of believers, and I do consider myself primarily a Catholic Christian, as there is more that unites us than divides: Devotion to Mary, which has been a very big part of ecumenical revival, affirmation of the ecumenical councils (some say the first 7, others 3 or 4), 3 creeds, 7 sacraments, the 3 ranks of holy orders, the church fathers and holy scriptures, apostolic succession. Veneration of Saints, Real Presence of Christ in the Eucharist, the historic liturgy, and shared ritual usages.