Can you tell me about the three ways planets are classified?

The eight bodies officially categorized as planets are often further classified in several ways:

-----by composition:
Terrestrial or rocky planets: Mercury, Venus, Earth, and Mars:
The terrestrial planets are composed primarily of rock and metal and have relatively high densities, slow rotation, solid surfaces, no rings and few satellites.
Jovian or gas planets: Jupiter, Saturn, Uranus, and Neptune:
The gas planets are composed primarily of hydrogen and helium and generally have low densities, rapid rotation, deep atmospheres, rings and lots of satellites.
-----by size:
Small planets: Mercury, Venus, Earth, Mars.
The small planets have diameters less than 13000 km.
Giant planets: Jupiter, Saturn, Uranus and Neptune.
The giant planets have diameters greater than 48000 km.
The giant planets are sometimes also referred to as gas giants.
-----by position relative to the Sun:
Inner planets: Mercury, Venus, Earth and Mars.
Outer planets: Jupiter, Saturn, Uranus, Neptune.
The asteroid belt between Mars and Jupiter forms the boundary between the inner solar system and the outer solar system.
-----by position relative to Earth:
Inferior planets: Mercury and Venus.
Closer to the Sun than Earth.
The inferior planets show phases like the Moon's when viewed from Earth.
-----Earth.
-----superior planets: Mars through Neptune.
Farther from the Sun than Earth.
The superior planets always appear full or nearly so.
-----by history:
Classical planets: Mercury, Venus, Mars, Jupiter, and Saturn.
Known since prehistorical times
visible to the unaided eye
-----modern planets: Uranus, Neptune.
Discovered in modern times
visible only with optical aid
-----Earth.
-----The IAU has recently decided that "classical" should refer to all eight planets (Mercury through Neptune, including Earth but not Pluto). This is contrary to historical usage but makes some sense from a 21st century perspective.