A frittata is closer to a Spanish tortilla than our familiar omelettes. It always has another ingredient besides eggs; the entire mix is flipped over in the pan and not folded; it is cooked at a lower temperature and comes out firmer (some add flour), and served in slices. Some are more like a quiche.
Frittatine implies small ones, except for frittatine napoletane, common in Neapolitan friggitorie (snack shops). These aren't omelettes at all, but croquettes of pasta, egg, cheese and ham fried in breadcrumbs.
There are a zillion recipes (Italians especially like them with wild greens such as luppolo or vitabla).
frittata di erbe: made with fried onions, cheese, and wild herbs such as confenon (Friuli)
frittata di pasta: a popular way to use up leftover spaghetti, with grated cheese, ham, mushrooms or anything else
frittata rognosa made with a soft sausage such as ciauscolo or salame cotto.
frittata di scammaro: Neapolitan fast day dish of scrambled egg and pasta. The ancestor of spaghetti carbonara.
frittata in trippa: 'fake tripe' a thin frittata rolled up and sliced, then covered with a light tomato sauce to resemble trippa alla romana. Also called uova in trippa. Popular in Lazio and the Marche and Tuscany, where it's called frittatine trippate.
Image by jeffreyw