For recent converts/reverts like myself, seeing all of the acronyms and names of Mass types thrown around can be very confusing. If I understand correctly…
Novus Ordo = Ordinary Form (OF) = Mass of Pope John VI
Tridentine Mass = Extraordinary Form (EF) = Traditional Latin Mass (TLM)
Is this right? And are there any other acceptable current forms of Mass in the Latin rite (doubtless there are many more for our Eastern Catholic friends)? Any other names or acronyms I ought to know?
Pope John VI reigned from 701-705. Obviously you mean Pope Paul VI.
Other than that you have the synonyms correct, though there are varied levels of accuracy to those names.
The Ordinary Form used to be called the New Mass. As time goes on this term is becoming very rare, but you may come across it in things from the '70s and '80s. Another term one occasionally encounters is “Pauline Mass.”
Once in a while you will hear people refer to the Extraordinary Form as the Mass of John XXIII. I suppose logically it could therefore be called the “Johannine Mass.”
As for other forms of the mass in the Latin rite Church, first of all there are non-Roman rites like the Ambrosian Rite (Milan), Mozarabic Rite (Spain), and the Rite of Braga (Portugal). Then there are various alternative forms, or “Uses”, of the Roman Rite, such as the Anglican Use (recently returned Anglican communities), Dominican Use (Order of Preachers), Carthusian Use (Carthusian Order) and Sarum Use (England; virtually extinct). These Uses are often loosely called “rites.”
EF is also sometimes called the Tridentine Mass or the TLM - Tridentine Latin Mass. Within the EF, there are also two different forms: a low Mass (not sung), and a high Mass (sung - this is the usual Sunday liturgy). These are all the ones that I’m aware of.
In the Ukrainian Catholic Church, there are two forms that I’m aware of: the Divine Liturgy of St. John Chrysostom (ordinary form), and the Pontifical Divine Liturgy of St. John Chrysostom (used for when the bishop comes).
Regarding the Tridentine Mass, there is also the Missa Cantata, which is basically in between a Low and High Mass. It has singing, as the name implies. One could also talk about the Pontifical High Mass, which is a High Mass with the bishop (contrary to popular perception the word “pontiff” just means “high priest”, i.e. any bishop not necessarily the Pope). A High Mass with the Pope is called a Papal High Mass, not that I’m aware of this ever happening after the promulgation of what we now call the Ordinary Form.