Types of astronomical objects:

star celestial body that by itself actively emits radiation, of which the energy being internally produced by nuclear fusion
planet primary satellite of the Sun, with the property of having enough gravity that it formed itself into a
round shape, having succeeded in clearing its orbital neighbourhood
IAU definition
of the terms
planet,
dwarf planet,
plutoid, and
small
solar-system body
dwarf planet like "planet", but not having succeeded in clearing its orbital neighbourhood
plutoid dwarf planet outside the orbit of Neptune
small solar system body primary satellite of the Sun, with not enough mass to be planet or dwarf planet: asteroids and comets
comet small solar-system body, which at least in the part of its orbit near the Sun develops a coma by fumigating The precise
definition
and
delimitation
of these terms,
one of each other,
has not yet been
decided by IAU
asteroid small solar-system body, that is not a comet
MB-asteroid "Main Belt" asteroid = small solar-system body with semi-major axis between Mars and Jupiter
TNO "Trans-Neptunian Object" = small solar-system body with semi-major axis larger than Neptune (i.e. > 30 AU)
plutino TNO with 2:3-resonance to Neptune, like Pluto
TNO/Ha.fam. TNO and member of the collisional family of Haumea
TNO/1:2 TNO with 1:2-resonance to Neptune, sometimes called Twotino
SDO TNO with orbit in the "scattered disk" (semi-major axis > 50 AE)
SDO/2:5 TNO with 2:5-resonance to Neptune
"moon" small celestial body that primarily does not orbit the Sun, but an other celestial body A satellite of a satellite.