The word egg is a Viking word. (The Viking share of the English Language) They invaded England more than a thousand years ago. Some of them stayed and mixed their language with English. The English have many ways to cook eggs and many words for them.
In Western food hard boiled eggs are common in salads and sandwiches. There are special cups for soft boiled eggs called egg cups. There are different methods of cooking hard and soft boiled eggs with a cold or hot water start. Very gently boiled eggs are called coddled eggs. Boiled eggs mixed with spicy flavours are called devilled eggs. If cream or curry is added, they are called creamed eggs or curried eggs. Instead of using a frying pan, eggs can be cooked in an oven. These are called shirred eggs or baked eggs.
Hard boiled eggs can also be pickled. England and Germany are famous for their pickled eggs. These are eggs that sit in vinegar or brine (salt water) for several weeks. China also has many types of pickled eggs.
Fried eggs cooked on one side are called sunny side up. Those cooked on both sides are called over easy. These two terms are more common in the US and Canada; they are still seen as Americanisms in the UK. When the white and yolk are mixed they are called scrambled eggs. Sometimes the egg can be put in a hole in a piece of bread and fried. This is called toad in a hole in the US and eggy bread or eggs in a basket in the UK. If you see toad-in-a-hole in a Western restaurant, do not expect to eat a toad. (In the UK, the same name, toad-in-a-hole, is also used for another dish: sausage cooked in Yorkshire pudding.) Sometimes the egg can be fried in water, instead of oil; these are called poached eggs. I make poached eggs in soup.
An omelette is a special type of fried egg. The eggs are mixed up with a little milk and then fried slowly. Many interesting vegetables and meats can be added. A farmer's omelet contains potato, ham, bacon, sausage and onions. The Western-Chinese version of a farmer's omelet is called eggs foo yung (芙蓉蛋). It has bean sprouts instead of potato and less meat. There are many overseas versions of eggs foo yung with many different vegetables and meats. A fluffy omelet has many air-pockets in it and is made by mixing the whites separately, then adding the yolk.
There are some special types of egg dishes. A meringue is a sweet egg white coating used to cover pies. Eggnog is a flavoured sweet-milk drink with raw egg. Eggs a la reine are eggs for the queen. It is a poached egg with mushrooms and cheese. Eggs a la Lee are a US variant of Eggs a la reine with ham and mushroom sauce. Eggs Benedict is a poached egg on a toasted English muffin with a slice of ham and Hollandaise sauce. There are many more.
Humans have eaten bird eggs since prehistoric times. They are common all around the world. There are many English variations on these names and I could go on for pages.