The most obvious non-technical difference between upright (also known as vertical) pianos and grand pianos is that verticals have a smaller footprint and usually cost less. Grands are more likely to be purchased for their value as room-enhancing furniture, take up more space, and cost more. In fact, many who don’t play or play very little buy a grand as much to make a statement about themselves as for any other reason.
Technically, however, there are very big differences between verticals and grands. The action (key-and-hammer mechanism) of the grand is specifically designed to increase the speed and reliability of repetition (the ability to repeat notes in rapid succession) and the ability to control the volume of sound. Verticals are usually inferior in this regard. The sound of the grand bounces off floor, wall, and other surfaces, and is diffused by them, before reaching the player’s ears, whereas the sound of the vertical tends, literally, to be in the player’s face. The end result of these differences is that grand pianos usually produce a more pleasing sound and can be played with greater expression. That said, there are some phenomenal high-end verticals out there that can run circles around some lesser-quality grands.
For more information, see Piano-Buying Basics: Vertical or Grand?