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.
fritta di erbe: made with fried onions, cheese, and wild herbs such as confenon (Friuli)
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.