That’s an excellent question (thanks, Christine G.). The distinctions between cakes, layer cakes, tortes, tarts and gâteaux are rarely discussed. Most people simply assume they’re just different words people use to describe the same things, but that’s not really true. The distinctions between them can be fine but they’re real and worth noting. I’m not aware of any definitive resource on the subject, so all I can do is try to create my own. Pastry enthusiasts, chime in if you want to add or correct anything.
Cakes are single-layered sweetened and enriched “breads” for lack of a better word. Usually round and almost always flat, their primary ingredient is grain or grain flour (wheat, oat, barley or the like). Cakes can be sweetened with sugar, molasses or honey and enriched with eggs, solid fat or oil. They can be leavened naturally (yeast), mechanically (egg foam) or chemically (baking powder or soda).
Layer cakes are the same thing as cakes, only stacked on top of one another, then filled and iced. Compared to straight “cakes”, which are mostly an Old World thing, layer cakes are a mostly New World thing. They’re almost always leavened chemically.
Gâteaux are French and have more in common with pastries than they do cakes, since they’re composed of multiple thin layers. Their structural layers are usually sponge cake. Their remaining layers can be made of creams, jams, fruits or mousses — some of which are thicker than the baked layers that support them.
Tarts are flatter, simpler pastries with a short crust base. The can be filled with fruit, chocolate, creams, jams, just about anything you can think of. Normally they don’t have a top crust like a pie, but then sometimes they do!
Tortes split the difference between tarts and gâteaux, at least in my mind. They’re flat — or at least flat-ish — but typically have a sponge cake base. They tend not to be as complex or amply filled as gâteaux, and their batters tend to have a higher proportion of ground nuts. They can be either single-layer or multi-layer.
There. Not exactly academic, but at least I’ve stuck a flag in the dirt. As I said, all those who care to add anything, please chime in.