As it is generally used today, in the context of creationism (most specifically young earth creationism), it can be called "neo-catastrophism" or the "new catastrophism" (a term coined by early proponent George McCready Price in his 1923 book The New Geology). Though, even among creationists, it is often just shortened to "catastrophism."

Also, in reference to the importance to the Biblical flood, it is sometimes called "flood geology" (which can either refer to the flood as the only catastrophic cause or just the most important one). It is the idea that geology/geologic column and especially the fossil record are the result of catastrophic forces (the Genesis deluge almost exclusively).

From the www.rae.org (The Revolution Against Evolution) glossary for "catastrophism" (my commentary):

Belief that geologic history is dominated by a catastrophe or catastrophes, such as the Cataclysm. [the Noachian flood]
Interestingly, in a typical creationist ploy at chumming the waters with misinformation, it defines "Neo-catastrophism" as:
Belief that earth has suffered major geologic catastrophes in the past, but with great spans of time passing quietly in between them.
This 'progressive ages' between catastrophes better describes the ideas of Georges Cuvier than the philosophy of later creationists.
Uniformitarianism is assumed as much as possible.
Uniformitarianism has never absolutely eliminated the idea that changes can result from catastrophic events, i.e., flood, tsunami, vulcanism—only as the primary or only cause for geologic change. This is like the argument that evolution breaks the SLOT, when in fact, the theory does provide for local decrease in entropy as long as the overall amount does not.
The standard belief of most geologists today.
Highly misleading, since while geologists do accept forms of catastrophic change, characterizing them this way intends to make them appear friendly and accepting of creationist ideas (thus making those ideas appear scientifically credible).

Similarly, Stephen Jay Gould (along with Niles Eldredge) and punctuated equilibrium are paraded out as somehow supporting catastrophism because of his problem with strict gradualism and the idea of periods of rapid evolutionary change (that is, "rapid" in a geologic sense).

Not a proponent of " hopeful monsters," he has written an essay critiquing Charles Lyell and his push for uniformitarianism. An essay that has been quote-mined in order to make it appear Gould rejected it, when in fact, it was the methods Lyell used promoting a strict, or what in Gould's words was a "methodological" uniformitarianism. Also he was pointing out that catastrophism was "more scientific" (obviously with qualification) in the sense that it was much more easily testable.

[Gould will often write essays where he will look at people whose ideas have been rejected and find positive qualities in their work, in the end better showing how science should/shouldn't work, saving the person from historical ridicule, and making more interesting reading. But even Richard Dawkins, who is no fan of Gould and has criticized him often, openly admits Gould to be no saltationist.]

While the above strayed somewhat from the topic, it does illustrate how a scientific idea (whether accepted or refuted), such as Cuvier's catastrophism, can be twisted to meet another end.

Catastrophism in the context of creationism first made a real impact among several Seventh Day Adventists (Price was). It was rejected by many of the other believers of special creationism, at the time—largely due to the "taint" of being promoted by Adventists, a group many of the fundamentalists and evangelicals disliked (or worse). Many of the early scientific creationist groups were composed mostly of Adventist members.

But the idea caught on. Standing back from all the details and controversies, one has to admit that it nicely ties up any difficulties that so-called secular (often " naturalist" or " atheistic") science has found with an acceptance of a historically acurate, literal Genesis narrative. Without much knowledge of geology, it does seem to explain why fossils and mountains and whatever are the way they are. Most importantly, it gives the idea that those beliefs are scientifically valid, which is a great comfort, much the same way that the belief that the New Testament (and Old) is historically accurate does (historicity is somewhat beyond the scope of this writeup, but it is interesting how important that and the need for scientific credibility remains for people whose religion values faith as paramount).

As the creationist movement grew during the 20th century, along with it came catastrophism. But it didn't really "break out" as a primary tenet of the philosophy/worldview until 1961, when John C. Whitcomb Jr. and Henry M. Morris published the seminal The Genesis Flood, which set forth catastrophic ideas in a popular way (though still written in a way to preserve the idea that the concept is scientifically valid). Not only a popular success, part of its breakthrough was that it was from more "mainstream" creationists (read: non-Adventists) and thus more easily accepted. From there many of the early and even some still extent groups formed to discuss, study, and promote scientific creationism. Catastrophism, particularly catastrophism that is specifically flood-oriented, became a standard belief for most creationists.

Catastrophism is also a simple way to reject the logical conclusions of uniformitarianism, which is necessary in order to reject the evidence for, among other things, an ancient earth and evolution (especially human evolution).

Another interesting thing on the subject is the work of the Russian pseudoscientist Immanuel Velikovsky, who viewed catastrophism on a cosmic scale. While not working from a strictly religious perspective, he did begin with the assumption that the Bible was historically accurate. On the other hand, he takes into account religious myths from any number of civilizations and accepts them as accurate representations or allegoric representations of actual astronomical phenomena.

Excerpts of his work from Skeptic's Dictionary at http://skepdic.com (page numbers correspond to his 1950 book Worlds in Collision):

Under the weight of many arguments, I came to the conclusion—about which I no longer have any doubt—that it was the planet Venus, at the time still a comet, that caused the catastrophe of the days of Exodus (181).

When Venus sprang out of Jupiter as a comet and flew very close to the earth, it became entangled in the embrace of the earth. The internal heat developed by the earth and the scorching gases of the comet were in themselves sufficient to make the vermin of the earth propagate at a very feverish rate. Some of the plagues mentioned in Exodus like the plague of the frogs...or of the locusts, must be ascribed to such causes (192).

The question arises here whether or not the comet Venus infested the earth with vermin which it may have carried in its trailing atmosphere in the form of larvae together with stones and gases. It is significant that all around the world people have associated the planet Venus with flies (193).

The ability of many small insects and their larvae to endure great cold and heat and to live in an atmosphere devoid of oxygen renders not entirely improbable the hypothesis that Venus (and also Jupiter, from which Venus sprang) may be populated by vermin (195).

His "evidence" primarily comes from the story of Athena springing from the head of Zeus (to him, Venus and Jupiter, respectively). Refuted early on by science, his work is still given credence by those in some of the fringe sciences and other pseudosciences. His ideas are also incorporated as validation for the more purely creationist catastrophism.

[It should be noted that there is school (in only a loose sense) of belief among some scientists that strongly stresses the importance of cosmic collisions in the history—geological and biological—of the earth that refer to themselves as neo-catastrophists. By and large (whether they are right or not in their conclusions) they are real scientists and not to be confused with creationists or believers of Velikovsky's pseudoscience.]

(Sources: a great deal of reading on the subject, including Gould and Dawkins; of particular help is Ronald L. Numbers' 1992 excellent and evenhanded study The Creationists: the evolution of scientific creationism)