Spaghetti is cooked in a great pot of salted, bubbling water then emptied in a colander (scolapasta in Italian).
In Italy, spaghetti is for the most part cooked but still firm (Italian for to the tooth), just completely cooked and still firm. Outside Italy, spaghetti is off and on again cooked to a much softer consistency.
Spaghettoni is a thicker spaghetti which sits down for a bit to cook. Spaghettini and vermicelli are extremely slender spaghetti (both of which may be called holy messenger hair spaghetti in English) which sit down to cook.