There are quite a few different classifications for planets based on different factors. Important facts include size, mass, mineral or gas composition, and distance from other celestial bodies (by which some bodies officially become "moons" instead of "planets"). Rocky planets, such as Earth, are differentiated from gaseous planets, such as Jupiter, because of their composition; Jupiter has a rocky core but its major mass is its atmosphere, while Earth's atmosphere is a small part of its overall mass. Generally, planets are either rocky or gaseous, with some having a large combination of the two; there are no officially recognized classifications for a planet's habitability, or different atmospheric content.
Pluto, always considered a full planet, was recently downgraded to "dwarf planet" status because it has not fully cleared the space in its orbit; this decision continues to create controversy.
I can answer your question if you are referring to the names of the groups that some planets belong to. There are many ways to classify these planets. If you look at the link that I provided for reference, you will see these classifications. However, speaking in the most general terms, there are two main "groups" of planets: Inner, which is also sometimes called Terrestrial, (includes Mercury, Venus, Earth, and Mars), and Outer, which is also sometimes called Jovian (includes Jupiter, Saturn, Uranus, and Neptune). Of course, Pluto is no longer a planet, it is now considered a "dwarf planet." Hope this helps...