A fighter is an aircraft whose role is to seek and destroy other aircraft whereas Bombers are aircraft whose primary purpose is to carry and deliver air to ground weapons.
Fighters are relatively very fast, carry a smaller payload (usually air dominance weapons), extremely agile/maneuvrable and often the first to enter in the theater of war to establish air dominance over a certain area whereas bombers carry a huge payload, are generally slow (travel at subsonic speed), are big, less maneuvrable and often used at later stages of the war when complete air domination is attained and there is little or no risk of enemy fighters.
