I use the twin phrases "the autocephalous movement" and "the independent movement" to describe a category of diverse, newer, smallish, self-governing apostolic-succession Christian church denominations that are not connected to (or formally recognized by), for the most part, the larger, older, apostolic-succession churches *. Some folks also use the terms, "Autocephalous Orthodox", "Independent Catholic", "Continuing Anglican", "Alternative Catholic", "Old Catholic" and "Traditionalist Catholic".
This is a "movement" only in the sense that it continues to evolve, grow and take root, and that these churches all take seriously their shared heritage of the tactile, historic apostolic succession. It is not a "movement" in any organizational sense -- the vast majority of these churches have no ties to each other.
Some of these churches are autogenic or self-starting: entepreneurial Christianity at its New Testament best! Others were created by splits (schisms) from a parent Christian denomination. Still others were left stranded due to political machinations in their parent churches.
Some have a "Roman Catholic" look, feel and texture (whether post-Vatican II or "traditionalist"). Others a more "Orthodox" feel. Some others, an "Anglican" feel, or sometimes even an "evangelical" feel. Still others have a "blended" feel. And some have a look-and-feel all their own.
And while their disciplines and liturgies vary, most of these churches embrace Christian theology that is both fairly catholic and orthodox. Somes of these churches are theosophical. And still others are, well, interesting.
The vast majority of these churches ordain married men, only a few do not.
Some of these churches ordain women, some do not.
Some of these churches ordain gay and lesbian folks and others do not.
* These older, larger apostolic-succession churches include the Roman Catholic Church, the Orthodox Communion, the Anglican Communion, the Old Catholic Communion/Utrecht, those Lutheran churches which retained their apostolic succession (Church of Sweden, Church of Estonia, Church of Finland) and the several ancient churches in the Middle East, Africa and India.