Meat 1
It is a common misconception, and often argued wrongly by vegetarians, that the use, in the English language, of pig/pork, calf/veal, cow/beef, sheep/mutton etc. has something to do with euphemisms used by meat-eaters pretending they're not eating animals. This is not the case.
In mediaeval England the peasants were Anglo-Saxon but the aristocracy was Norman-French; this followed the conquest of England by William of Normandy (France) in 1066. The aristocracy compelled the peasants to look after the animals but rarely allowed them eat any meat.
The peasants called the animals by the Anglo-Saxon names -- pig, calf, sheep, etc., but the aristocracy, who ate the meat, called it by the French names for the same animals -- porc (pig), veau (calf), boeuf (ox or bullock), mouton (sheep). This got Anglicised slightly over the centuries but this distinction between these animals and the meat has remained in every English-speaking country around the world. Animals which were not commonly eaten by the Norman-French aristocracy, e.g., chicken, turkey, rabbit etc., have the same name for the animal and the meat.
Meat 2
The word "meat" was commonly used, in 16th/17th century England, in the way that we now use the word "food". There are some interesting examples of this in the Bible where the Greek word "broma", meaning "food", was translated in the King James version, as "meat".
This created some oddities such as Genesis 1, 30: "I have given every green herb for meat". Since Adam and Eve had never eaten meat this doesn't make sense unless it reads "I have given every green herb for food". Which is how the English at the time of King James would have understood it anyway.
This was not a mistranslation of the Bible, as some have claimed. The translation at the time was perfectly correct, it's just our usage of 'meat' which has changed.
Vegan
The word was invented by the UK Vegan Society in the 1940's. They pronounced it "vee-gn". This is the most common pronunciation in the UK today. No one can say this pronunciation is "wrong", so this is also the politically correct pronunciation.
In the US, common pronunciations are "vee-jan" and "vay-gn" in addition to "vee-gn", although the American Vegan Society says the correct pronunciation is as per the UK usage.
The UK, and US and other places have other pronunciations.
This is sometimes a touchy subject, so be prepared to change your pronunciation.... (from the rec.food.veg FAQ)
Vegetarian
The term "vegetarian" was coined in 1847. It was first formally used on September 30th of that year by Joseph Brotherton and others, at Northwood Villa in Kent, England. The occasion being the inaugural meeting of the Vegetarian Society of the United Kingdom.
The word was derived from the Latin "vegetus", meaning whole, sound, fresh, lively (it should not be confused with "vegetable-arian" -- a mythical human whom some imagine subsists entirely on vegetables without nuts, fruits, grains, etc.!).
Prior to 1847, non-meat eaters were generally known as Pythagoreans or adhering to the "Pythagorean System", after the ancient Greek "vegetarian" Pythagorus.
The original definition of "Vegetarian" was "with or without eggs or dairy products" and this is the definition still used by the Vegetarian Society today. Most vegetarians in India, however, exclude eggs from their diet as did those in the classical Mediterranean lands, such as Pythagoras.
Some background to 'vegetarian' and 'vegan'
The earliest non-meat-eaters that we know anything much about were in India and Ancient Greece (Pythagoreans), they used plant food plus dairy products - what we would now call lacto-vegetarian, which has always been, and still is, the predominant form of vegetarianism in India.
The use of eggs was added by the British, probably in the 18th century when they revived the Pythagorean ideas. We can't be entirely sure why eggs were added but in the relatively cold, damp climate of Northern England, where all this was happening, the variety of fresh plant foods would have been much more limited than in India or the Mediterranean. Imports would have been very expensive and not very fresh by the time they arrived, so accepting eggs may have been a pragmatic decision. We would now call this group ovo-lacto-vegetarians and they are still the predominant tradition in the UK.
In 1847 the word 'vegetarian' was invented by Joseph Brotherton and friends - the founders of the UK Vegetarian Society. Before that they rather innacurately called themselves Pythagoreans but no-one seemed to be too concerned about accuracy until the V word was invented, and we've been arguing about it ever since. The original definition was about eating various plant-foods, not eating 'meat, fish or fowl' and the immortal final phrase: 'with or without eggs or dairy produce'. Hence the lacto-veg and ovo-lacto-veg.
Those who ate neither eggs nor dairy produce became known as 'strict vegetarians' and those remained the three main groups for the next hundred years or so.
However... as early as 1851 there was an article in the Vegetarian Society magazine (copies still exist) about alternatives to leather for making shoes, there was even a report of someone patenting a new material. So there was always another group who were not just 'strict vegetarians' but also avoided using animal products for clothing or other purposes - naturally they wanted their own 'word' too, but they had a long wait.
In 1944 Donald Watson and friends invented the word 'vegan' to fill the gap, and founded the Vegan Society (in the UK) specifically for this group. They defined the word in terms of all animal products, not just a diet, as that was the reason for inventing it, and everyone was happy - until the Americans got involved...
The British ideas had long since crossed the Atlantic but, as always, Americans have their own way of doing things. Whilst many used the same words, for the same reasons, even more began to use them differently. The health aspect of vegetarianism has always seemed to be a bigger issue in America than in Britain, and a lot of people who only ate meat occasionally, for health reasons, started calling themselves 'vegetarian'. The latest surveys suggest that, in the USA, there are up to seven times as many of these 'semi' vegetarians as genuine vegetarians by any of the definitions above.
For many, the logic of the health argument also leads to the removal of eggs/dairy products and it would appear that a very much higher proportion of American vegetarians are 'no eggs/dairy' than in Britain, but again a significant proportion of those are primarily motivated by health, and are therefore not bothered about wearing leather etc. This fits the 'strict vegetarian' group, but in the best of American traditions, they then confused things further by insisting on calling themselves 'vegan'.
This has become so common that the UK Vegan Society has had to acknowledge the development of its original word into concepts of 'dietary vegan' and 'ethical vegan', even though 'dietary vegans' are almost unknown in the UK, or anywhere else outside of North America.
"another fine mess" as one eminent American might have said...