Like long range escorts or intercepers
It's really hard to answer such a broad question without broad generalizations. The types of aircraft produced during the war boiled down the interaction between perceived strategic priorities and the capabilities and structures of the aviation industry itself. Most of the aircraft produced during the war stemmed from state contracts and competitions in which representatives from military-dominated bureaus would issue a call for an aircraft that can perform X functions, use Y engines, and have a range of Z and so forth. The various aviation firms would then tender their own answers to this design challenge. The requirements often fit the various conceptualizations of strategic needs of the time. Some of these needs were reflective of strategic realities that faced air planners. The Japanese Navy knew that operating across the Pacific would require a great deal of range and issued a 12-shi tender for a bomber that would exceed the range and speed of the Mitsubishi G3M Type 96 with the similiar engines, the resulting Mitsubishi G4M Type 1 bomber met these ambitious requirements, but at the expense of armor and converting the wing into something approaching a massive fuel tank. Other tenders were based on focus of military planners for certain types of aircraft. For example, under the influence of Ernst Udet, the Reichsluftfarhtministerium became briefly preoccupied with dive-bombing requirements for future bombers in the late 1930s as it was thought that this would be a more efficient use of aircraft because dive bombing was more accurate than level bombing. This meant that Junkers, Heinkel, and Dornier had to tender bomber designs with the structural strength to do engage in shallow dives. This met with limited success (the Ju-88 and Do-217) to outright disaster (the He-177). Of course, this is a highly simplified narrative and sometimes the research in industry would have an impact upon the military orders. North American's developed an alternative fighter design in house using data and engineers from Curtiss's P-40 program. When the British approached North American over the license production of P-40s, North American replied that they had a design better than Curtiss, the NA-73X- which eventually became the P-51. Other aviation firms would inform the military counterparts on developments in research and try to get them to incorporate them into future procurement. The first jet aircraft, the He-178, was developed in-house at Heinkel and later demonstrated to RLM's decision makers to encourage jet aircraft orders. RLM was unimpressed, and Heinkel began the development of the He-280 jet fighter as a private venture.
The limits of aviation industry acted as a straightjacket for certain type of aircraft. Although Walter Wever was an advocate of strategic bombing, the Luftwaffe cancelled its four-engine strategic bomber program in the mid-1930s because the RLM decided that German aviation industry could not produce enough high-end engines in the numbers needed to field a large four-engined bomber force. Italy's air force often had to field aircraft that served a dual purpose of symbolizing the fascism's modernity by breaking speed records and other barriers. Because the Italian aviation industry was relatively small, this politicization of design meant a series of compromised designs. This perhaps reached its nadir in the Breda Ba.88 Lince, whose stripped down prototype featured prominently in fascist propaganda but was capable of little else. This lack of balanced development meant that when the balloon went up in 1939, the Italians were unable to field indigenous aircraft designs that were competitive in appreciable numbers. The Macchi C.200 and Fiat G.50, the chief frontline fighters in 1939, were both underpowered and underarmed compared to their European contemporaries, but when reengined with German engines, these planes became more capable. German assistance allowed the Italian industry to achieve its potential, but it was hostage to political fortunes of Italy's northern neighbor.
This is just scratching the surface of aviation development during the war as each nation's industry and air arm was relatively unique.