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An oval is generally regarded as any ovum (egg)-shaped smooth, convex closed curve. Convex means that any chord connecting two points of the curve lies completely within the curve, and smooth means that the curvature does not change rapidly at any point. The ellipse is a typical oval, but a very particular one with a shape that is regular and can be exactly specified. It has two diameters at right angles that are lines of symmetry. It's best to reserve the word ellipse for real ellipses, and to call others ovals.

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The ellipse was first studied by Menaechmus, investigated by Euclid , and named by Apollonius . The focus and conic section directrix of an ellipse were considered by Pappus. In 1602, Kepler believed that the orbit of Mars was oval; he later discovered that it was an ellipse with the Sun at one focus. In fact, Kepler introduced the word "focus" and published his discovery in 1609. In 1705 Halley showed that the comet now named after him moved in an elliptical orbit around the Sun (MacTutor Archive). An ellipse rotated about its minor axis gives an oblate spheroid, while an ellipse rotated about its major axis gives a prolate spheroid.