There are essentially four different types of digital piano on the market today.
Upright digital pianos
Ideal for players at any level, upright digital pianos are designed for home use and are just as much a piece of furniture as they are a piano. A traditional cabinet design tends to be popular as it resembles the look of an acoustic upright piano and will have a built-in music desk, lid and integral stand with backboard and pedals. If you prefer a more modern look, some manufacturers offer a contemporary cabinet design where the lid acts as a music rack when open and covers the keyboard when closed, providing a sleek, low profile appearance. These pianos, while still classed as upright digital pianos, tend to be known as compact pianos as they invariably occupy less floor space.
Portable digital pianos
Similar to an upright digital piano but without the cabinet, a portable digital piano can be stored away when not in use or used away from home. This type of piano can be placed on a simple cross frame stand or sometimes on an optional matching stand. Unlike an upright digital piano, the speaker system is located in the actual piano itself rather than the cabinet. This ensures portability and low weight but at the expense of sound quality. An upright digital piano will have bigger and better speakers housed in the integral stand where there is more space. Also, the sustain pedal and music desk is usually detachable.
Stage digital pianos
Stage pianos often have a heavier, more robust body, and are better able to withstand the stress of gigging. Generally, most stage pianos do not have built in speakers as they are normally used with a keyboard amplifier or PA system. In addition, a stage piano will have features aimed specifically at the live keyboard player like the ability to mix and blend lots of sounds at once, the ability to edit and create your own sounds plus the ability to control other keyboards in a rig. Built for the stage and not the home, their appearance can be quite functional.
Grand digital pianos
Finally, if you love the look of a grand piano, then you can have the features of an upright digital piano in a baby grand case. Not only do you get the appearance of a traditional grand piano, you also get the best sound possible as the bigger cabinet usually houses a flagship speaker system.