There is no difference between a video card and a graphics card; however, there is a difference between a video card and integrated graphics, and basic knowledge of computer hardware can help you understand the benefits of a video card.
The main component for any home computer is the motherboard. All other major hardware plugs into the motherboard, including the CPU (Central Processing Unit), RAM (Random Access Memory) and a graphics or video card, if it is present.
Integrated graphics means that the computer's ability to process visual data, such as in movies and video games, is handled by the motherboard. The benefit of integrated graphics is that it's less expensive than buying a standalone video card, but at the cost of decreased video performance. If the most complex visual processing you need your computer to do is watching a movie, integrated graphics will probably be sufficient.
Video games have much higher processing demands for visual data. Integrated graphics will usually have lackluster performance in computer video games because it uses the resources from the CPU and RAM, which slows down the entire system. Graphics cards solve this problem by providing separate hardware that can plug into the motherboard dedicated solely to video processing. Video cards have their own processing (CPU) and memory (RAM) to conserve valuable resources, and generally even a low-end one will outperform almost any integrated graphics.