1)are graphics & video cards the same thing?
2)Do I need to buy a new monitor.
Technically no, the colour bit quality is defined by the graphics card not the monitor. Though a nice new screen may allow you to appreciate the improved performance of a new graphics card.
3)update my graphics card.
On the face of it, this would be the most appropriate solution, but first find out what Mother Board you have so that you can work out what sort of card is required, probably AGP. Don't go overboard when you chose.