You may have also seen the word "omelet" written as "omelette." Both are the same except "omelete" is considered more American English.
Deviled egg is commonly seen here in the US. To make it, the egg would be boiled and then the egg yolk would be removed to be added with mayonnaise and mustard. It is then added back into the boiled egg white. It's served cold and is delicious.
Tea egg is probably more common in Asian countries. It is known as egg boiled in tea and some other spices to make it very flavorful.
What's your favorite kind of egg style?