After some digging, looking up high-school biology and checking Cantonese culinary terms, we think we have cracked this question. It is probably worth setting out all the related terms here as well.
牛雜－a popular street food in south east Asia which involves stewing beef offal in a rich sauce made from Chu Hou Paste 柱候醬. The offal found is limited to what's inside the abdomen like intestines, lungs, spleens, kidneys, livers and stomachs, but no brains or hearts.
金錢肚－Within a pot of 牛雜, this is perhaps the most recognizable due to its honeycomb appearance and perhaps the most popular. It is more appropriately named in English as the honeycomb tripe and comes from the second stomach, the reticulum, of a cow.
牛栢葉（牛百頁）－An ingredient sometimes found in 牛雜 but more often missing because it is a dish in its own right. This perennial favorite dim sum dish is from the third stomach, the omasum (aka manyplies), of a cow. The dim sum version is bleached white using hydrogen peroxide (an industrial chemical that's also used in the bleaching of dark fish meat in fish fingers to make them commercially more desirable.) The hotpot version is normally unbleached and appeared blackish. It is known as leaf tripe in English, referring to the leafy texture of this particular stomach.
牛肚－This is from the first stomach, the rumen, of a cow. It is known as smooth tripe in English and perhaps the least desirable of the three types of tripe. As found in the quote from The Deluxe Food Lover's Companion (Deluxe Edition)
The tripe found in most markets today is the lining of beef stomach, though that from pork and sheep also fall under the definition. There are two beef stomach chambers and three kinds of tripe, all of which are tough and require long cooking. The best tripe, from the second stomach chamber, is called honeycomb tripe because the inner side has a pattern similiar to a honeycomb. It's the most tender and subtly flavored. Pocket tripe is cut from the end of the second stomach chamber. It's shaped like a pocket with the inside also being honeycombed. The least desirable plain or smooth tripe (with a smooth texture on both sides) comes from the first stomach. Tripe is available fresh (which is actually partially cooked by the packer) in most supermarkets. Choose tripe with a pale off-white color and store for up to a day in the refrigerator. Tripe is also available pickled and canned. The most famous French dish using this variety meat is the Norman dish called tripes à la mode de Caen-tripe braised with carrots, onions and cider. In Spanish-speaking countries, menudo (tripe soup) is a well-known favorite.
牛胃－The all inclusive term covering all the above, plus the reed tripe from the fourth stomach, the abomasum, of a cow.
Update - if you like this entry, please check out our latest write up on beef from our blog, thank you.
So now you have the answer to the above question and more. We are all for knowing what you eat.
Related wikipedia links:
hydrogen peroxide bleaching of dark fish meat