Most gnocchi are tiny potato dumplings -- Florentines call them topini, or field mice, which gives an idea of their size -- that one briefly boils, and then seasons with a sauce, for example Sugo alla Bolognese in winter, Tomato sauce with a dollop of unsalted butter and some shredded basil, in summer, and Pesto sauce, when it's really hot.
Gnocchi alla Romana are a completely different animal; they're made with milk and semolina, and baked. They're also extraordinarily tasty, to the point that Artusi, who knew a good thing when he saw one, introduces them with, "I hope you will like these as much as my guests have. If you do, toast me if I'm alive, or say a Rest in Peace if I've gone to push up cabbages," and goes on to say, "They say the number of people at table should never be fewer than the Graces (3), nor more than the Muses (9). If your party's nearer the number of the Muses, double the recipe."
Excellent advice, though there is some controversy surrounding the dish: Livio Jannattoni, one of the great Roman gastronomes, says he grew up with potato gnocchi, and first encountered semolina-based Gnocchi alla Romana on a dining car far from Rome, where they took him completely by surprise.
Regardless of their origin, Gnocchi alla Romana are now firmly established. They are also easy to make, and one of those dishes that one can enlist the assistance of a small child in preparing. In short, a perfect introduction to cooking!