In the RBFF guidebook interview, the game's staff were asked about why they updated 'Real Bout' by changing the layout of the buttons. They responded:

"In Fatal Fury 3 we introduced the Oversway Line. It seemed to be very difficult for new players, but we were convinced the idea itself was good. So we tried to make it easier to use this game, which meant adding a dedicated button for it. That was the biggest reason for changing the entire button layout."

Having three attack buttons also corresponded to having weak, mid, and strong attacks, which matched their vision of the game being simple to understand, but deep.
Contributed by ProtoSnake
In the RBFF guidebook interview, the game's staff were asked about the meaning of the title “Real Bout”? And they responded:

"That was actually the working project title of the original Garou Densetsu. As this development progressed, we wracked our brains trying to come up with a new title for this sequel, and wondered if changing the entire title itself wouldn’t be more interesting. Then someone suggested, “hey, what if we bring back ‘Real Bout’…” So we have a lot of attachment to it, as you might imagine."
Contributed by ProtoSnake
The Ring Out mechanic had several scrapped iterations. These included being frozen, falling off buildings, and being consumed by animals when outside of the ring.
Contributed by ProtoSnake
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SNK created new assets for the loading screens on the Neo-Geo CD version. However, the art style used for said loading screens was considered "too eccentric" by many fans, to the point that they sent letters directly to SNK demanding that they shouldn't use the style anymore. Because of this, the art style used in those loading screens was never used again in future SNK games.
Contributed by ZpaceJ0ck0
The team originally wanted to include a brand new character into the game. However, because of Billy Kane's popularity among fans, they scrapped this idea and added Billy instead.
Contributed by ZpaceJ0ck0
This game was originally planned to be the final chapter in the Fatal Fury series, but the game was successful enough to dismiss this plan.
Contributed by ZpaceJ0ck0
Cheng Sinzan was originally going to appear in the game as a playable character, but Duck King was chosen over him in the end.
Contributed by ZpaceJ0ck0
The "ring-out" mechanic added to the game was heavily criticized by arcade players as it was possible to lose a match with only a single mistake such as blocking from an enemy attack, or side-stepping behind the enemy only to fall out. Because of this, the ring-out feature was removed from future games in the series.
Contributed by ZpaceJ0ck0
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In the Neo Geo AES/MVS version of Real Bout Fatal Fury, Blue Mary can be seen topless if she falls into the water, this was cut in the PS2 version.
Contributed by ProtoSnake