Both mugs and cups are generic terms used to describe drinking vessels. Mugs are generally large, thick-walled vessels that have a handle. The handle makes them easier to hold and drink from, since they are usually used to hold hot drinks like coffee, tea, or hot cocoa. To retain heat, they are often made of ceramic or stoneware.
Cups, on the other hand, typically do not have a handle. They are generally shaped like a cylinder or a fluted cylinder. They are often made of glass or plastic, and are suitable for drinking cold beverages. Often, they are transparent in color to allow you to see the cup’s contents.
