Historically, several aircraft were designated bomber destroyers prior and during the Second World War. They were interceptor aircraft dedicated to destroy enemy bomber aircraft with exceptionally powerful armament. They were a generally intended for day use, so were a separate category from the existing night fighters.
The United States considered powerfully armed destroyers, like the Bell YFM-1 Airacuda prototype, to counter a potential attack of high-performance bombers. The Lockheed P-38 Lightning and Bell P-39 Airacobra were also designed with the aim of mounting very heavy armament, including 37 mm guns, in the anti-bomber role. Great Britain, by contrast, favored specialized "turret fighters", such as the Boulton Paul Defiant, which mounted heavy armament in a rotating turret.
A deceptively similar, although completely different, designation was the German Zerstörer (meaning "destroyer"). Introduced on 1 May 1939, the term did specifically exclude the defensive anti-bomber role (leaving it for the light fighters), and envisaged a heavy fighter for offensive missions: escorting the bombers, long-range fighter suppression, and ground attack.
Since then, improvements in both engine power and armament generally led to a loss of interest in this class for most nations. Even small fighters were able to carry enough firepower to deal effectively with enemy bombers. This remains true even today.