All our modern peas are descended from the wild pea, Pisum sativum, which is still found in the Middle East, though the subspecies which gave rise to the garden pea, probably in Afghanistan or nearby, is apparently extinct. The remains of seeds of this species have been found in Stone Age sites from Greece, Turkey and the Middle East. Around 3000 BC, they show up in European sites, showing that they were being cultivated outside their original range. Later the Field Pea was developed, an improved type with larger seeds, which became a medieval staple.
All peas were originally round-seeded. When dried, they are, as the name implies, round, with little or no wrinkling. They're full of starch, which feeds the seedling while it establishes itself. They're filling, but not so sweet as Tesco's frozen peas. So they're not what you really want for that little green pile on the side of your plate. Originally, they were grown in the fields to provide dried peas for pea soup, mushy peas, pease pudding and the like, providing an important part of the diet. Namissa's West African, none of us like English cooking much, and they're ideal for the type of food we do like, curries, African dishes, and the like. So they suit us. In the garden, they're as tough as old boots, and can safely be planted in autumn for a spring harvest.
Until the 19th Century, the rich used to eat sweet young peas when they were in season, and leave the mature version for the hoi polloi as far as they practically could. Around 1820, a wrinkled pea appeared as a chance mutation in a field of peas. There seem to have been earlier wrinkled varieties, but it was from then on that the great 19th Century advances in pea breeding took place, so it has to be seen as significant. It has far more sugar than the older types, as it's not metabolised into starch so efficiently. This made it possible to breed the sweet-tasting, large seeded marrowfats which are so familiar today. They're tender plants which have to be planted in warm soil, as the seeds rot easily. Their appearance, combined with the development of glasshouses which made it possible for those with money to extend the season, led to the continuing popularity of the green pea, a crop which has never been particularly high-yielding.
Yields are greatly reduced by the virtual disappearance of the tall varieties which were the mainstay up till the middle of last century. Tall peasticks became ever harder to find, and as a result the tall varieties, which often reach six or seven feet, started to disappear. This was exacerbated by stupid laws which forbid the sale of seed of unregistered varieties, the cost of registration, and seed companies which develop crops with farmers in mind, then flog them to gardeners. Farmers, of course, want something which can be harvested by machine, and that means one which is short enough not to need support. So the average seed catalogue nowadays has about half a dozen short peas, where a Victorian one would have pages of peas, many of them tall.
Tall varieties are still around if you look. Alderman is still commercially available, and is one of the best. Other varieties are available from smaller suppliers like Robinson's, Real Seeds and Brown Envelope Seeds. Real Seeds charges 1p for membership, so they're not selling to the general public, others ignore the law. apart from those, a lot more are available from sources like the HSL or seed swaps.
Purple-Podded Peas are old-fashioned field peas. They're not as sweet as the green-podded ones, though many have wrinkled seeds. I suspect most go back to the 19th or early 20th Century. On the whole, they don't have fancy names, either because they've been lost, or because they were bred by farmers and gardeners rather than by seed companies.
Umbellate peas are a curiosity. Sweeter varieties appeared in Italy in the 17th Century, and became popular on the continent. Charles II took a fancy to them when he was in exile, and brought them with him when General Monck invited him to become king. The umbellate peas date to this era. They have wide, flattened stems (the technical name for this is fasciation), branch at right angles to the main stem, and have all the flowers at the top. The only one I've come across is the Salmon-Flowered Pea.
Mangetout peas lack the hard membrane lining the pod, and have been bred for sweet pods which can be eaten whole when the peas are small. There are two types; snow peas, with flat pods, and sugarsnaps, with round pods.
Petit Pois are bred to provide very small peas. I find it hard to see the point when large varieties like Magnum Bonum are as sweet as anything!