Understanding the question as asking:
1) In what context are all these labels used? 2) what do they signify? 3) and what is their canonical status according to the RCC? 4) Are some or all of them considered schismatics by the RCC?
About the following groups/labels:
1.Traditional Catholics [Catholics who identify themselves as Trads] 2. SSPX - Society of St. Pius X. 3. Opus Dei 4. 'Ultra-Conservative'. 5. Jesuit. 6. Conservative 7. Liberal 8. 'Neo-Catholic'. 9. [Roman Catholic in the] Personal Ordinariate of Our Lady of Walsingham in the UK 10. Eastern Rite Catholic.
The Eastern Rite Catholic lady belongs to one of the Eastern Rites [Churches] of the Catholic Church;
Mr. Andrew Leach belongs to an ecclesiastical structure called a Personal Ordinariate in the Roman Rite of the Catholic Church;
Opus Dei is a Catholic Institution that is a type of an ecclesiastical structure called a Personal Prelature in the Roman Rite of the Catholic Church; and
Pope Francis belongs to the Religious Order of the Jesuits in the Roman Rite of the Catholic Church.
As regards, their canonical status, all of the above are Catholics - the expression more Catholic than the Pope comes to mind - in the Catholic Church. The Eastern Rites and the Roman Rite are Catholic Rites in the Catholic Church, the ecclesiastical structures were conceived and created by the Catholic to further the mission of the Catholic Church, and the Religious Orders are approved by the Church as ways for individuals to achieve sanctity and serve the Church.
SSPX - The Society of St. Pius X, is an international priestly society founded in 1970 by the late Archbishop Marcel Lefebvre in the diocese of Fribourg, Switzerland. The members are all Catholics but currently, the society does not have a canonical status within the Catholic Church. During the pontificate of Pope Emeritus Benedict XVI, SSPX was offered the canonical status of a Personal Prelature as part of a deal to heal the group’s rift with the Catholic Church. The deal fell through. It is unclear whether they are in schism since there appears to be no formal declaration from the Vatican in this regard. A Catholic ought to consult with their Ordinary regarding SSPX.
The labels do not have any significance and meaning in the Catholic Church. One is a [faithful] Catholic or not, and that includes the Pope.
Understanding the Church terminology above
The various Rites [A Christian rite, in this sense comprises the manner of performing all services for the worship of God and the sanctification of men], are or have arisen from the three major groupings of Rites based on this initial transmission of the faith, the Roman, the Antiochian (Syria) and the Alexandrian (Egypt). I personally see the stamp of St. Peter, the first Pope on these first three Rites.
The Church sets up ecclesiatical structures to futher her mission. The Personal Ordinariate was erected to enable (groups of) Anglicans to enter into full communion with the Catholic Church, and a Personal Prelature is a juridical structure introduced by the Second Vatican Council. The Council decree Presbyterorum Ordinis stated that, among other institutions, “special dioceses or personal prelatures” could be established “to carry out special pastoral tasks in different regions or among any race in any part of the world”.
Within the Church, there are innumerable ways as there are individuals or stars in heaven to achieve sanctity and express holiness within the Church, the ways to manifest the holy in the One, Holy, Catholic, and Apostolic Church, and that's why there has arisen over the course of the life of Church religious orders [cf. Religious Life | New Advent] like the Jesuits.
This variety and diversity in the Church, in its Rites, in its Ecclesiastical Structures, and in the Vocations/Callings of her children, can best be summarized by:
“In essentials, unity; in non-essentials, liberty; in all things,
charity.” - St. Augustine of Hippo.
We are now left with the Labels - There isn't a 'page and line' for any of these in the Catholic Church!
As for the labels Conservative and Liberal (and the others in the spectrum: ultra-conservative, moderate, progressive, etc.), these seem as from the US sociopolitical landscape and a lens through which those familiar with them, attempt to understand and thereafter apply to individuals and groups in the Church.
Traditionalist/Trad is the label some Catholics identify with. They describe themselves as being or wanting to be the Catholics of the pre-conciliar Church.
Note: Wikipedia applies this label to SSPX and SSPX speaks of itself as 'firmly embracing a traditional, Catholic worldview'.
A Neo-Catholic as a term coined by Mr. Gerry Matatics and popularized by Mr. Chris Ferrara in his book The Great Facade, is:
[A] combination of conservative and liberal elements representing a
progressive tendency overall. They are not usually the cause of
liberalism but enablers of the liberalism in the Church [...].