The significant distinction is between "occult" and "not occult," which has been described by various terms, including both "public" and "manifest." A non-occult heretic is outside the Church according to the majority view.
Van Nort has something on this which I can get for you. And Father Cekada speaks of the distinction being between "occult" and "not occult":
For the latter, the various theological and canonical treatises did not always use an identical term, but instead employed a variety of expressions to describe the papal heretic or his heresy: “public,” “notorious,” “manifest,” “openly divulged,” etc.
These were generic terms that did not have a uniform meaning in sources and authors before the 1917 Code, and were simply used in contradistinction to “occult.” (See F. Roberti, “De Delictis et Poenis,” schemata praelectionum [Rome: Lateran 1955] 80–1) Authors writing after the 1917 Code about the question of a heretical pope continued to use the same generic language to distinguish between occult and non-occult heresy.
Because of this, Fr. Boulet and many others like him have fallen into anachronism about the terminology. They mistake this generic language used by authors writing about papal heresy before the Code, and subsequently taken up even by authors after the Code, as an indication that all the minute criteria of the Code’s criminal legislation must be satisfied before a loss of papal office can kick in.
This, alas, is a fatal error, so none of their arguments on this point can be used against the sedevacantist case.
If you want to argue about a distinction of theological significance between "public" and "manifest" to ahead; I"ll obviously read it.
There is a principle that the Roman Pontiff is above canon law
. This means that whatever terms are used, they are not canonical terms. When St. Robert Bellarmine said, "manifest" heresy, and St. Francis de Sales said, "explicit" heresy (in regard to a pope), they were not using canonical terms. St. Francis was even writing to Protestants, so he expected them to understand, which means he was using an ordinary human term, and one not difficult to understand. Today, post-Vatican II, people spend a lot of unnecessary time twisting and pulling at the ordinary term that was not meant to be difficult. This reminds me also of when St. Thomas Aquinas said as an ordinarily accepted principle, "it would be blasphemy to say that the Church does anything in vain"
, and, today, people claim it difficult to discern when we can say that "the Church" has actually "done" something! It's rather scary.
It appears both the aforementioned Saints and Doctors avoided saying "public" because that was an ordinary word they did not deem appropriate. You see, Pope John XXII held an error, and it was known by the public, yet he was not a manifest or explicit heretic. That is why I say the terms are not equivalent. Obviously, manifest
heresy is something more than merely being known by the community.