Just had a chance to research this a little and the minor variations are endless.
I reviewed recipes by Jacques Pepin, Julia Child, Joel Robuchon, Paul Bocuse, Gordon Ramsay, Guy Savoy, Auguste Escoffier, Alain Ducasse and Ann-Sophie Pic.
In its simplest form, the dish is thinly scalloped potatoes cooked in milk and seasoned with bay leaf, thyme, nutmeg and garlic, then browned in the oven.The garlic is not minced, but is used to wipe the oven dish.
Then there are other versions which include cream in the recipe. Some use more than others; some mix the milk with the cream to add extra richness.
Then there´s the cheese, which is usually added as a topping. Gruyère, Comté and even Cheddar are used.
Finally, there are recipes which add even more bits and pieces, like fennel fronds or breadcrumbs on top.
Not to be confused with gratin Lyonnaise, which is cooked on the stove top and has onions with it.