First, let me assure you that in real Life "catalog" works for me 95% of the time. Those catalogs devoted to books, garden seeds and cooking utensils are eagerly devoured. I understand that "catalog" is even an acceptable spelling in other countries now.
However, we've just never brought ourselves to drop the "-ue" from "catalogue" in art history and no one deviates from this unwritten decree. If anyone were to try it, my suspicion is that certain people in the field would snicker behind their hands and make snide remarks about Sears, Roebuck and Co. and outhouses. (Look, I don't make [let alone agree with all of] the rules in The Art World, but do take my indoor plumbing quite seriously.)
Also known as "sales catalogues," these list the lots included in any specific auction (past, present or future). They are published, to the tune of many thousands of new catalogues per year, by auction houses. Of prime importance are the numbering of lots and estimated going prices of each, so that readers know which lots to bid on and approximately how much money they'll have to spend.
Speaking of spending, these are not sales fliers. They are no less expensive to publish than other types of art catalogues, and so must be purchased. Many auction houses are now providing online versions, though, and these are available to browse if one registers (usually for free) with the firm's website.
Auction catalogues can be works of art, themselves, for great care is taken to illustrate the lots with high quality images. Additionally, these catalogues are treasure troves of information for researchers. Each lot is typically accompanied by pertinent details such as media, dimensions, artist, year of creation, venues in which it has been displayed, bibliographic citations and provenance or record of ownership.
Within the covers, the author details each piece's (1) provenance, (2) size, (3) current condition and (4) external publications in which the piece has been written up. Photographs and/or scans are a heavily prominent feature.
These are records of all of the items in a museum, gallery or private collection. In other words: inventory. Preferably computerized.
There are not very many full collection catalogues published; you'd need an appliance dolly to cart around bound lists of thousands and thousands of items. One must nearly always be physically *at* an institution in order to view its full collection catalogue - and this from a computer station in the facility. However, many museums do publish highlights of their collections, or highlights of collections-within-The-Collections (such as "Oriental Porcelains" or "European Sculpture").
Happily for us, the Internet has made most of these highlights easily accessible. Go to nearly any museum website, and there will be a "Collection" section to browse. Dependent on staffing and budget, some sites' online collections are exhaustive and include works not always on public display.
These are published in conjunction with temporary exhibitions, both those that travel (usually the case) and those that do not (in the event of a blockbuster one-off show). The key word here is "temporary." Although an exhibition may travel for years visiting many art museums, it will eventually be disbanded and all works on loan for the show will return to their private owners, collections and holding or permanent institutions.
Exhibition catalogues not only contain images and descriptions of the pieces on display, they are chock-full of essays typically written by the exhibition's curator and other specialists in the topic at hand. These articles provide physical, historical and biographical information that puts the show's theme in context.
You'll also find footnotes and bibliographies galore in any exhibition catalogue, and most contain indices and some section devoted to chronology. Many of these volumes - written by top scholars - are a researcher's dream, which is why art historians and enthusiasts buy, keep and refer to them with relish.
One will additionally find that even softcover versions of these thick, heavy catalogues are somewhat pricey. And that is why, Concerned Reader, that we mention (often) and review (as time allows) Special Exhibition Catalogues here at About Art History.
I hope this clears up any confusion about the word "catalogue" in an art historic sense. Thank you for writing and asking questions.