"Poached."This is an egg cracked open and gently boiled out of the shell until the whites have congealed but the yolk is still runny. Poached eggs are great with potatoes, toast, or corned beef hash due to the great amount of runny yolk left for spreading or dipping. Most restaurants advertising eggs “any style” will poach eggs but some prefer not to outside of breakfast hours, since it involves boiling at least a small saucepan of water.
"Scotch Egg." A Hard-Boiled egg that has been wrapped in Cumberland sausage and rolled in bread crumbs. Sometimes a soft-boiled egg is used.
"Hard boiled." Everyone knows what a hard boiled egg is: an egg boiled in its shell for 13-15 minutes until the whites are firm and the yolk is solid.
"Soft boiled." An egg boiled inside its shell, just like a Hard boiled egg, until the whites have set and the yolk has very slightly thickened. This is the “three minute egg” that gave us the three minute “egg timer”. PROTIP: It will continue to cook from residual heat within the egg, after you take it out of the water - run the egg (still in the shell) under some cold water immediately to stop the cooking process.
"Scrambled."This is the other one everyone knows: the egg white and yolk are mixed together, sometimes thinned out with milk, cream, or water, and fried. At Mexican restaurants this is “huevos revueltos”, found in Tucson on “Machaca plate” shredded beef combinations (at Nico’s or Los Betos, and many finer establishments) and inside breakfast burritos.
"Fried" or "Over hard and break ‘em."Just ordering a “fried” egg gets an egg fully fried on both sides, slightly browned, with a broken yolk. They are good on sandwiches but leave no yolk to spread on potatoes or toast. All following eggs are considered to be variations of ‘Fried’
"Over easy." What is usually thought of as a fried egg: pan fried on one side until cooked about halfway through, then flipped over and fried on the other side until the white has set. The edges can be a bit crispy but the yolk is still runny, albeit not so much as a properly done poached egg.
"Over medium." Like an over easy egg, but cooked a bit more on the second side. The yolk will be somewhat thick or sticky, but not hard.
"Over well" or "Over hard." An egg fried on one side as for “over easy”, then cooked on the other side until the yolk has completely set. Some cooks will break the yolk.
"Sunny side up." The egg is fried on one side and not flipped. Sometimes a bit of frying fat is spooned over the top to set the white, or some water is tossed into the pan and a lid placed over the egg. Both of these methods are called "Basted", but this isn’t universally understood if requested and often done by default anyway. Some cooks will leave the white on the top is left unset and sticky.