Digital zoom is used to simulate optical zoom. When you use digital zoom during picture-taking, the subject appears larger in the electronic viewfinder or camera screen. The same happens when you use optical zoom. Unlike optical zoom, digital zoom increases the apparent picture size through electronic interpolation of the pixels, resulting in a lower resolution of the captured picture.
Magnifying lets you enlarge a picture you have already captured. It is used while reviewing pictures on the camera, and does not alter the orginal picture.