There are 18,446,744,073,709,551,616 planets in No Man's Sky. All of the planets are actually planet-sized, and walkable, i.e. there are no gas giants. Each planet has one prevalent biome/weather type; It is entirely possible for a planet to be entirely covered in water or sand. Planets might have Earth-like features, such as canyons or mountain ranges, or rings around them like Saturn. The features of a planet are determined by procedural generation and concepts of physics, like the day/night cycle that is calculated depending on the position and rotation of it relative to any nearby suns, the color of the atmosphere depends on what elements are in it, and whether a planet has water or not is determined by factors such as how close the planet is to its sun.
One difference to our galaxy is the distance between planets in a solar system, which will be much smaller then in real life, to replicate traditional sci-fi depictions of alien planets.
Planets have points of interest and will get weirder and more dangerous as the player approaches the center of the galaxy.
Some planets shown in the demos have names containing the prefix "new" such as New Eridu, and some others are followed by a roman numeral, as in Darko IX.