Botanically speaking, not a whole lot, since they’re all part of the Musa genus. Once all fruits of that shape were known simply as “bananas”, the sweet yellow varieties like the Cavendish were called “dessert bananas.”
Plantains are a much starchier version of a banana. They’re larger, denser, and are rarely eaten raw (or in a sweet preparation). The neat thing about them is that they can taste radically different depending on when they’re eaten and how they’re prepared. The missus, having spent two years in the Dominican Republic, lovers hers fried. Being as starchy as they are, green unripe plantains are treated not unlike potatoes in much of the world. Sliced into thin rounds and twice-fried in oil, they’re terrific with garlic sauce (mojo). They can also be pan-fried after they ripen and sweeten to create an entirely different, soft and caramelly accompaniment to rice and beans. Plantains can be baked, made into soup, pie, what-have-you.