In computer graphics terminology, clipping paths is a term that refers to creation of an image with compositing one or more images in it. Basically, tracing out a shape by pen tool in Photoshop is termed as applying clipping paths to that image which means to cut it from the background in order to use it in some other image. On the contrary, the alpha channel saves the selection like a grayscale mask which is editable. For instance, if a part of image is selected, the unselected area is masked or you can say it is protected while you perform editing on the selected image and apply effects on it. This selection can be saved permanently with alpha channel.
There are some differences between clipping paths and alpha channel as mentioned below:
Alpha channel or simply transparency is applied to objects having soft edges, and feathering whereas clipping paths are used for objects that have hard edges
Clipping paths is used to isolate or protect area of an image while those masks are stored in alpha channel.
Clipping paths is a one bit mask which actually does not have any existence but alpha channel is actually a mask and it is a 32-bit graphic transparency system that consists of four channels including 8-bit channel each for red, green and blue and one 8-bit for alpha channel.
Mask created with clipping paths have sharp edges but alpha channels create soft edges and gradation level of transparency.
Clipping paths cannot preserve softness of an image having feathered edges but masks saved in alpha channels can be edited just like other images.