Fighting is normal feline behavior, but sometimes it's hard to tell if the pussies are actually playing or if it's for real. To distinguish one from the other, look at body language and the nature of the fight. When they're playing, for example, they take turns; but if they are fighting, interrupt with a loud sound or put a barrier between them.
Method 1 of 3: Observe Body Language
Step 1. Check for growls or hisses
When cats are playing, they don't make much noise; at most they meow.
If they don't stop hissing and growling, it's not a joke
Step 2. Look at the ears
In play, cats keep their ears forward or erect, or slightly bent back; on the other hand, if they're all the way back (almost touching their head), it's very likely to be a fight.
Step 3. Look at the claws
A playing cat's nails are hidden or retracted (much of the time), and even if they are exposed, they are rarely used to hurt the other.
Step 4. Check for bites
During a play fight, cats bite each other very lightly without causing any damage. But if you see that (at least) one of them is biting for real, be suspicious.
Howls of pain, hisses and growls are also bad signs
Step 5. Observe the body position
Playing, cats keep their bodies positioned forward; fighting, they alternate between attacking and bending backwards (to escape opponents' scratches).
Step 6. Look at the fur
When they are aggressive, cats keep their fur upright; it's an attempt to look bigger. If their tails are ruffled, maybe it's not a joke.
Method 2 of 3: Examine the nature of the fight
Step 1. See if there is reciprocity
When playing, cats take turns: both spend the same amount of time on top and bottom.
The same goes for chases: they intersperse between chasing and being chased, like a real tag
Step 2. Note the speed of attacks
Fighting games involve lots of breaks and starts, allowing them to rest and change position. Real fights, on the other hand, are much faster and neither of them stops until there's a winner.
Step 3. Pay attention to post-fight behavior
It says a lot about what just happened: after a disagreement, cats tend to avoid each other (or, at the very least, the grumpiest of them will).
If that doesn't happen and they continue behaving normally, they were just kidding
Method 3 of 3: Breaking the Fight
Step 1. Make a loud noise:
clap your hands or pans, slam a door, shout or use a whistle. Hopefully, that will be enough to distract the cats and end the fun.
Step 2. Create a barrier
This tends to work as cats lose eye contact. Put a pillow, a piece of cardboard, or any other object that blocks their view, and as soon as they stop fighting, put them in separate rooms until they calm down.
To prevent this from happening in the future, make them interact little by little
Step 3. Don't separate them with your bare hands
Want to put them in the middle of two aggressive cats to see what happens? It's not just your fingers that can get bitten and scratched: one of the animals (or both) can jump in your face.
Not to mention that they can redirect anger towards you, affecting the relationship you have even after the events
Step 4. Prevent future disagreements
Don't make them compete for resources: each should have their own litter box, food and water bowls, beds and toys in different parts of the house. Also know that neutered cats are less aggressive and therefore fight less.