A bicycle basket is a basket that is attached on a bicycle and used to carry freight, typically small items. They are typically used for little shopping tasks like making routine trips to the store for things like milk or fresh bread.
A bike rack that attaches directly to a bicycle is commonly known as a "bike rack," "bicycle rack," or "rear bike rack." These racks are designed to provide a platform or framework for carrying items on a bicycle, such as bags, panniers, baskets, or other cargo.
Bike racks can be mounted on various parts of the bicycle, but the most common type is the rear bike rack, which attaches to the frame or seatpost of the bicycle near the rear wheel. These racks typically have a horizontal platform or a set of bars with rails where bags or other cargo can be attached.