  We compare two ways of interpreting higher order connections. The geometric
approach lies in the decomposition of higher order tangent space into the
horizontal and vertical structures while the jet--like approach considers a
higher order connection as the section of a jet prolongation of a fibered
manifold. Particularly, we use the Ehresmann prolongation of a general
connection and study the result from the point of view of geometric theory. We
pay attention to linear connections, too.
