NO = novus ordo, or “new order”, abbreviated NO.
This was the name of the Mass that came out as a result of the work done at Vatican II. It’s the Mass that most people in the U.S. are familiar with, done in the language of the people (mainly English and Spanish in the U.S., although in this part of the country, we see a lot of Polish Masses).
EF = extraordinary form
OF = ordinary form
These are the names that the Pope uses for the two forms of the Mass. For this reason, many of us prefer to use these two names rather than novus ordo or NO. There are some Catholics who take offense to the term NO, becaues it looks like the English word, “No,” which has a very negative connotation. But a lot of Catholics don’t take offense, either, since the term is correct. The Mass is the “new order.”
The EF is the Latin Mass, or “traditional Latin Mass,” or “TLM.” This is the old form of the Mass that was done for many centuries. Pope Benedict XVI released a motu proprio a few years back that makes it very clear that it is OK for parishes to hold EF Masses without getting permission from the bishop (although practically, priests DO continue to seek approval from their bishop, because it makes for a more friendly relationship).
Before the motu, there were a lot of dioceses where the TLM was essentially “forbidden.” Pope Benedict made it very clear that the Latin Mass, or EF, was here to stay.
The OF is the same as the novus ordo, or “new Mass” or “verncular Mass.” The Pope has labelled this the “ordinary form” because it is the form that most people will be experiencing. Pope Benedict XVI has made it clear that this Mass form is also here to stay, not a passing fad.
The EF and the OF are the same rite (the Roman or Latin rite), but two different forms. They are both equally efficacious, and both equally reverent when done with liturgical correctness, free of abuses. It is totally a question of personal preference.
I hope this helps.
My husband and I are converts from evangelical Protestantism. Both of us prefer the OF, as to us, coming out of the evangelical Protestant tradition, understanding and comprehension are extremely important. We respect the EF, and those who prefer it.
We are blessed that there is a TLM parish in our city, where Latin Masses are held daily and several times on Sunday. The parish has about 400 people in regular attendance, while the OF parishes have 1000s in attendance. So in our city, the TLM has not attracted many Catholics. However, in other cities, I’ve heard on CAF that the TLM has become very popular, especially among younger people.