A partial loop connects the components provided in a path with each input component acting as a way-point on the path. The loop will always start with the first provided component and end with the last.
An extended loop is always created from just two components (or possibly one edge component). It finds a path between these two components, then extends that path at both ends. It extends each direction until it either hits a boundary in the geometry, or finds its way back to the existing path. Often the resulting path will neither start with the start component or end with the end component.
A closed loop is always created from just two components (or possibly one edge component). It always tries to find a path the goes from the starting component, passes through the end component, and then continues on looking for a path back to the starting component. The paths returned will generally both start and end with the starting component.