Path selection tool VS Direct selection tool

I'm assuming you're talking about Adobe Illustrator's Selection tool (the black arrow), and the Direct Selection tool (the white arrow). If so, you want to use the Selection tool when you're moving entire objects or paths, or selecting groups of objects. If you want to modify an object or path's shape, you need to use the Direct Selection tool, because it can select individual points on a path, which you can move to modify a shape or curve. Also, with the Direct Selection tool you can select one object inside of a group without selecting the entire group, so it's useful to modify something quickly without ungrouping.

So the Selection tool is used for moving or selecting entire objects or paths, while the Direct Selection tool is used more for modifying the shape of an object or path.