The path a free-falling object follows in curved spacetime is called a geodesic.
In general relativity, gravity is not treated as an ordinary force pulling objects through otherwise fixed space. Mass and energy curve spacetime, and an object in free fall follows the straightest possible path through that curved geometry. That path is a geodesic.
The idea extends the familiar straight line from Euclidean geometry. On Earth's curved surface, for example, the shortest routes are great-circle paths rather than ordinary straight lines on a flat map. In four-dimensional spacetime, geodesics describe the motion of freely falling particles and the paths of light.
The terms “orbit” and “worldline” are related but not interchangeable. An orbit is a particular kind of motion, often repeating around another body, while a worldline is the broader path of any object through spacetime. A null geodesic is specifically the geodesic followed by light, whose spacetime interval is zero. Massive freely falling objects follow timelike geodesics, and their motion can look accelerated to a distant observer even though they feel no gravitational force locally.