Author's note: I'm bored. I will try to keep it as concise as feasible.
So generally speaking the purpose of fighting systems in RPGs, mostly jRPGs but many wRPGs hold to this as well, is to be representative of battle that takes place in the world, at least to concerning the degree of abstractness of the system itself.
E.G. Persona 3, FFTactics, Kingdom Hearts.
While a developer's choice in a battle system is partly to fit the aesthetic and style of the game, and if they are good paying attention then it fits the environment of the game as well such as Paper Mario or Twewy, the technical limitations are an important factor, simply look at the Legend of Zelda series.
However, it is a misconception to think Real-Time systems and Turn-Based systems are distinct from each other. In reality, they are simply opposite ends of a spectrum, with ATB (Active Time Based) systems being in the middle.
The differences are mainly found in that of execution and controllability.
A TTBS (Tactical Turn Based Battle System) is a derivative of the Turn-Based battle system that utilizes its advantages to control an arbitrary number of characters at one time because it has the slowest execution speed. However, once execution speed increases, the amount of characters one can control must decrease significantly, ATBS might only have 4 controllable characters, and a Real Time system will usually be limited to one. While control over a character can remain constant more or less, its impossible to control multiple characters independently and simultaneously.
In other words, as excution speed rises towards real time, the amount of controllable characters sharply decreases.
Other than these two factors, everything else remains constant including possible complexity, depth (when describing the intracies of the combat system and its subsystems), degree of control on a single character at one time, player involvedness, scale, difficulty in programming, Etc.
With regards to the concern of Abstractness, the slower in execution a battle system is the more it tends to be abstract. This can easily be seen in TTYD vs Super Paper Mario. There are exceptions however, KH:COM and Re:COM are real-time but very abstract while a game like Chess, for lack of a better example, is turn based in the world it exists in so its not Abstract at all. Thus it varies based on developer preference but is heavily influenced by execution time, i.e the faster the execution time the harder it is for the combat world to be abstracted from the game world.
tl:dr: RPGs use the same battle system, turn-based and real-time are simply on a spectrum of execution time, how long player's have to carry out actions. Controllability, the amount of characters the player can control at one time decreases with rising execution time. Abstractness, the divorcedness of the combat's world from the game world is tied to execution time but not strictly, thus there are exceptions. Everything else is constant, a game will not be more strategic because its turn-based or more action oriented because its real-time.
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