The safety risks when using a elliptical are the moving parts to the elliptical which can injure fingers while the elliptical is in use. Health risks for the elliptical would be not to use extensively if you are pregnant.
As an elliptical orbit is any orbit that isn't perfectly circular, everything has an elliptical orbit. The planets Mercury and Pluto have the most elliptical orbits of the planets, and are easily seen to be oval shaped. Comets also have highly elliptical orbits.
An elliptical trainer is essentially they same thing as an elliptical. The difference is found in price and size. An elliptical trainer is generally for smaller spaces such as homes or smaller gyms were as a full elliptical is bigger and more expensive. They offer they same benefits.