Asian Carps: In the US, this term usually refers to certain carp species that have escaped from catfish farms into public waters, where they threaten native fishes:

Bighead Carp: Has a large, scaleless head (see here).

Black Carp: Feeds mainly on snails and mussels (see here).

Grass Carp: See White Amur.

Silver Carp: Known for jumping out of the water when threatened (see here).

White Amur: Occasionally used to control aquatic weeds; often called a grass carp (see here).

Common (European) Carp: Introduced from Europe in the 19th century, this is the most widespread type of carp in Texas; often reach 30 pounds or more (see here). Variants include:

Ghost Carp, or Ghostie: A cross between a metallic koi and a common carp (see here).

Koi: An ornamental Japanese carp (see here).

Leather Carp: A smooth-skinned carp, though a few scales may be present near the dorsal fin (see here).

Linear: A smooth-skinned carp with a row of large scales along the lateral line (see http://www.phpaide.com/?langue=fr here).

Mirror Carp: A carp with very large, irregular, and patchy scales (see here).

Buffalo: Native to Texas, buffalo are actually suckers, not carp:

Bigmouth Buffalo: Similar to smallmouth buffalo with a thicker body and a forward-facing mouth (see here).

Black Buffalo: Closely related to the bigmouth buffalo, the black buffalo is darker and has a more horizontal mouth with thicker lips (see here).

Smallmouth Buffalo: Most common buffalo in Texas; looks like a gray carp with large black eyes and no barbels (see here).

Other Carps, Suckers, and Carplike Fish:

Barbels: Small carp-like fish found in Europe and Central Asia (see here).

Crucian Carp: A small member of the carp family found in Europe and Asia (see here).