What are the differences between Trachinotus and Bramidae species?
Pomfrets comes from the order Perciformes (the largest order of fishes) and are part of the Bramidae family. They strictly live in marine environments, mainly the Atlantic, Indian, and Pacific Oceans. They have a dorsal fin extending over the length of the body in some and anterior dorsal fin spines unbranched. 

http://www.fishbase.org/summary/FamilySummary.php?ID=319

Pompano comes also comes from the order Perciforme and are part of the Carangdide family which includes jacks, mackerels, scads, and runners. Most are fast-swimming predatory fish that hunt in the waters above reefs and in the open ocean. They also mainly live in marine environments such as the Atlantic, Indian, and Pacific Oceans, and are rarely found in brackish waters. Their body is generally compressed, although body shape extremely variable from very deep to fusiform. 

Quote about Pompanos from Fishbase.org:


  Most species with only small cycloid scales. Scales along lateral line often modified into spiny scutes. Detached finlets, as many as nine, sometimes found behind dorsal and anal fins. Large juveniles and adults with 2 dorsal fins. Anterior dorsal fin with 3-9 spines; the second having 1 spine and usually 18-37 soft rays. Anal spines usually 3, the first 2 separate from the rest; soft rays usually 15-31. Widely forked caudal fin. Caudal peduncle slender. Pelvic fins lacking in Parona signata. Vertebrae 24-27 (modally 24).


Unfortunately, I can only post one link due to my rep, but it fairly easy to search fishbase.org for information on both species.