Hybrids, or Aviation Surface Combatants, are warships designed with features from both gun-fighters and aircraft carriers of any sort, also known as Flight-Deck Cruisers, Heavy Aviation Cruisers, Flight-Deck Battleship or Battle Carriers, are warships created to strike targets from afar with aircraft, yet capable of engaging into gunfights to some degree, they can be considered as cheaper and (theoretically) more sustainable alternative to Missile Cruisers and even heavy-gun-armed variants of an Arsenal Ship.
Depending on purpose and builder's preference, Aviation Surface Combatants can be built in aviation-oriented, gun-fighting-oriented configurations, or balanced between these two:
Similar to carriers accommodated with main guns from large surface combatants or surface combatants with a large through flight deck, their main strength lies on their large air group just like ordinary carriers but also have medium to large caliber guns to exchange fire with other warships. Because of that, this type of aviation surface combatants could be built with lesser armor and guns than conventional surface combatants with similar size and weight class.
Built with the intention of attacking their opponents with both aircraft and guns simultaneously, this type of aviation surface combatants is generally better armed and armored than the aviation-oriented type, some of them may have hanger to shelter the planes from gunfire and air strikes. Depending on what purpose(s) it will serve, the number of aircraft on board can vary from a token size of 10 or less for mission grinding, submarine hunting and just for fun, to around 20+ for basic PVP requirement (e.g. against light carriers).
Aviation vessels with protection closer to a gun-fighting type and gun-fighting capacity closer to an aviation-type, this type of aviation surface combatants normally kites the targets at afar and only closes in to pick off survivors after air strike, yet still capable to directly engage one if necessary, but as a typical "jack of all trade" they will have difficult time to fight a full carrier with similar strength (i.e. more planes) or a pure battleship with very heavy AA batteries.
By Ship and Armament Size
In a nutshell, a flight-deck cruiser is an aviation surface combatant using a flight deck with runway(s), accommodated with 200-400mm armor, main guns with caliber up to 203mm (up to 30.5cm in-game) and up to 30+ AA/DP guns (estimated base on Aviation Cruiser IJN Mogami), the size of its air fleet will be 4-18 plane (estimated base on Andrea Doria and Moskva Class Helicopter Cruiser) for ASW only and PVE, and 20+ plane (estimated base on typical light carriers) for low to medium tier PVP requirement, speed is the key asset as one will found itself rely on kiting or hit-and-run tactics while using aircraft to keep the opponent too busy to dish out heavy damage on it.
A real-life counterpart would be the British UXV Combatant Concept, with V-shape flight deck and runway, a 155mm rapid-firing main gun, 20 VLS and 1-4 CIWS (AA and anti-surface), and "large number" of aircraft (UCAV in this case). The fleshly converted USS Lexington (CV-2) and USS Saratoga (CV-3) also came close to this category for their 203mm main guns and armor up to 178mm (belt and bulkhead), but it was their purpose distinguished them from the flight-deck cruiser we talked here.
Heavy Aviation Cruisers and Flight-Deck Battleship
An aviation surface combatant with heavier armor (400-600mm) and guns than a flight-deck cruiser, with the latter achieved by increasing the caliber (356-381mm), the size of its air fleet would be normally around 20-30+ plane, depend how you fight and who you are going to face, this type will either fight like its lighter cousin or fight its opponent head-on.
No real-life counterpart is/was present, but there is a French Jean Bart hybrid carrier proposal (some had described it as a Bague Carrier glued to the back of the fore-part of Jean Bart, armed with 1-2 380mm quad) mentioned in some documents and forums can be considered as one. On the other hand, the Heavy Aviation Cruiser classification of Kuznetsov-class is mainly based on her usage and to deceive the missile-preferring Khrushchev, not because she WAS built as one.
A larger cousin of the flight-deck battleship that is essentially a battleship modified to accommodate a flight deck capable of holding 30-40+ plane, yet still has 3-6 battleship main guns (380-460mm) to sink any ship that does not armored to withstand gunfire from battleships. Just like a flight-deck battleship, the battle carrier can swarm its opponent by aircraft and either pick off what has left or engage in a gun-fight.
No real-life counterpart is/was present, but the concept is frequently used on space warships in many sic-fic.