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 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. Frittatine simply implies small ones, though in practice either can be any size.
There are a zillion recipes; some are more like a quiche.
frittata di erbe: made with fried onions, cheese, and wild herbs such as confenon (Friuli)
frittata rognosa made with a soft sausage suchas ciauscolo or salame cotto.
frittata di scammaro: Neapolitan fast day dish of scrambled egg and pasta. The ancestor of spaghetti carbonara.
frittatina di verdure: with chopped greens or other vegetables
frittatine napoletane, common in Neapolitan friggitorie (snack shops) aren't omelettes at all, but croquettes of pasta, egg, cheese and ham fried in breadcrumbs.
Image by jeffreyw