Since these are all recipes, I think it would e a mistake to try to translate them. For example, we have "sweet corn mash" in English, but it's not the same thing.

"Canjica" is a kind of corn, usually white but also yellow. and it can also be a sweet corn mash with the same name.
"Canjicão" is a semi-sweet dish made with milk, canjica, and cinnamon - similar to sweet corn mash in English
"Canjiquinha" is a dish that includes pork chops

Recipes:

Canjica. Deixe de molho o milho da canjica de véspera. No dia seguinte, leve ao fogo na mesma água em que ficou de molho. Junte o cravo ea canela, o sal e leve ao ...
receitas.maisvoce.globo.com/Receitas/.../0,,REC979-7777-68+CANJICA,00.html -

Canjicão
Receita de Canjica Cremosa com Coco - canjica e deixe de molho por alguma horas. Cozinhe na panela de pressão por 40 ou 45 minutos com 1/2 litro de leite, ...
cybercook.terra.com.br/receita-de-canjica-cremosa-com-coco.html

Canjiquinha, Ingredientes: 400 gramas de canjiquinha 1 quilo de costelinha de porco 3 tomates 2 cebolas 1 molho de salsa e cebolinha 2 colheres de sopa ...
www.cozinhabrasileira.com/suinos/canjiquinha.html

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Note added at 36 mins (2009-10-19 22:05:54 GMT)
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I was working on this answer when Judith posted hers.

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Note added at 40 mins (2009-10-19 22:09:49 GMT)
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By the way, hominy is not a plant, it's corn cooked in a certain way. I'm not certain that canjica is exactly the same thing as hominy.

Hominy
A food made from hulled corn kernels soaked in lye water, rinsed, then cooked and eaten; or, the rinsed kernels are dried and coarsely ground into hominy grits
en.wiktionary.org/wiki/hominy

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Note added at 13 hrs (2009-10-20 11:08:20 GMT)
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Based on Fernando's excellent link, here are suggested English equivalents, with a level 4 certainty!

canjica: dried dent corn kernels
canjicão: popping corn / popcorn / mushroom corn kernels
canjiquinha: grits

The above products are all natural and unprocessed.
Hominy, on the other hand, is the result of a process, essentially the same as nixtamalized corn - see explanation at the end.

Examples of dent corn:

Dent Corn is used a great deal in processed corn foods, such as breakfast cereals, cornmeal, corn oil, corn syrup, hominy, posole and starch. ...
www.practicallyedible.com/edible.nsf/Pages/dentcorn

Corn Pops is a breakfast cereal made by Kellogg's, described by the company as " crunchy ... Britannica online encyclopedia article on dent corn (cereal), ...
www.cooktrix.com/search.php?keywords=Corn Cereal

... directly from the stored grain, usually yellow dent corn, without any pretreatment. ... They're used to manufacture breakfast cereals, snacks, and beer, ...
books.google.com/books?isbn=0684800012...

Examples of "mushroom corn kernels"

Jun 24, 2009 ... In addition to the Land O'Lakes products, The Big Popper uses only the highest quality mushroom corn kernels, which are the very best for ...
www.reuters.com/.../idUS188666 24-Jun-2009 MW20090624 -

Gourmet Popcorn Store - The Big Popper
The finest quality mushroom corn kernels (the very best for making popcorn), go into our unique 460° giant air popper. The intense high heat makes them not ...
www.thebigpopper.com/aboutus

Hominy / nixtamalized corn:
From Wikipedia
Nixtamalization typically refers to a process for the preparation of maize (corn) in which the grain is soaked and cooked in an alkaline solution, usually limewater, and hulled. The term can also refer to the removal via an alkali process of the pericarp from other grains such as sorghum. Maize subjected to the nixtamalization process has several benefits over unprocessed grain for food preparation: it is more easily ground; its nutritional value is increased; flavor and aroma are improved; and mycotoxins are reduced. These benefits make nixtamalization a crucial preliminary step for further processing of maize into food products, and the process is employed, using both traditional and industrial methods, in the production of tortillas, tamales, corn chips, hominy and many other items.