Web development covers the whole creation of a web application / web site - the back end (servers, connections, backups, updates, etc.) as well as the front end - the user interface, user experience, the 'work flows' (how the app / site will be used), among other things.
On the other hand, web designing is concerned with front end - looks, feel, and usability. It involves creating user personas, wireframes, mockups, and user testing.
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