How do various traditions define the term "sufficient grace"? I have read various polemics on the topics of Augustinianism, Calvinism, Jansenism, Pelagianism, Arminianism, and Catholicism which seem to use the term "sufficient grace" in different ways. For instance, this blog post by a Catholic claims that James White misuses the term "sufficiency of grace," and that White is ignorant of the history of Jansenism's denial of the Catholic doctrine of sufficient grace. However, it seems just as likely that White is simply using the term in a different way.

What is an overview of how the term "sufficient grace" has been used by various perspectives in these debates?
If you do research on Calvinism, Jansenism, Pelagianism, etc., you might find the term "sufficient grace" bandied about. The trouble is, depending on who's using it, it's defined differently, which makes it a not terribly useful term. So I'll try here to clear up who uses the term and what they mean by it.


Catholics and Arminians use the term "sufficient grace" as a synonym for "prevenient grace" as a way of saying that prevenient grace is sufficient to save if it is cooperated with.
Some Calvinists (such as James White) use the term "sufficient grace" as a synonym for "irresistible grace" as a way of saying that God's grace is always sufficient to save if he intends it to save.
Jansenists (17th century Catholics who were condemned as Calvinists by the Catholic Church) use the term "sufficient grace" in the Catholic sense, but only to critique it. They denounce it as "merely sufficient" (as opposed to effectual), and call prevenient grace "little grace," since it is powerless to save.
Similarly, some Calvinists (such as Charles Hodge in all three volumes of his Systematic Theology) use the term "sufficient grace" in its historic sense in order to describe Arminian teachings on prevenient grace. However, they would still claim that it actually makes grace insufficient to save on its own (see last bullet point).
Augustine, whom Jansenists and Calvinists both claim as their early forerunner, used the term similarly to both groups, drawing a distinction between "sufficient grace," given to all men, and "efficacious grace," given only to the elect.
Catholics and Arminians claim that the Calvinist doctrine of common grace (grace which can lead to conviction of sin, but not to salvation unless accompanied by saving grace) denies the sufficiency of grace for salvation.
Calvinists claim that since Catholics and Arminians believe that grace does not save unless it is accompanied by an exercise of the will (which does not always occur), Arminians functionally deny that grace is sufficient.


In my opinion, due to the diversity of thought, it is better to use the specific doctrinal terms -- prevenient grace, common grace, irresistible grace -- rather than the easily misinterpreted term "sufficient grace."

Sources:


Eastern Orthodox appraisal of Augustine on sufficient grace
Charles Hodge's Systematic Theology on CCEL: Vol 1, Vol 2, Vol 3
Catholic description of the Jansenist heresy
Catholic appraisal of James White's use of the term, along with historical notes on Jansenism (the blog post linked in the question)