Comets are often classified by their orbits, individual
classes having similar orbital periods, or aphelia and/or perihelia.
An overall classification is between short-period comets
(aka periodic comets) versus long-period comets,
based upon whether their perihelia are less or greater than 200
years. Some subgroups of short-period comets:
Halley-type comet - orbital period between 20 and 200 years.
Jupiter-family comet - orbital period less than 20 years, with an orbital plane relatively close to the ecliptic (within 30°).
main belt comet - orbiting within the main asteroid belt, but showing comet characteristics.
Encke-type comet - with an aphelion of less than 4 AU.
Some subgroups of long-period comets:
near-parabolic comet - eccentricity slightly less than 1, generally, a period of 1000 years or greater.
hyperbolic comet - eccentricity more than 1: those with eccentricity only slightly more than 1 are presumed to be solar system objects, but those with significantly more are taken to be interstellar objects.
Sungrazing comets are those that come very close to the Sun
(irrespective of their orbital periods).
Some subgroups of sungrazing comets:
Kreutzer sungrazer comets (perihelion on the order of 0.005 AU, and an orbital period around 750 years, and orbital inclination of 144 degrees, i.e., retrograde).
Meyer sungrazer comets (0.035 AU, a decade, 72° ).
Marsden sungrazer comets (0.044 AU, 5.6 years, 13° ).
Kracht sungrazer comets (0.049 AU, 3-4 years, 26° ).