A magical fireball is just a large mass of high energy, or rather a chaotic state if excited particles. Normal flames require a fuel that will have kinetic energy when flying in a direction, resulting in an explosion of sorts, with the kinetic energy of the fuel dispersing to surrounding particles and creating heat. What if there is no fuel to lead to that reaction? Would the two fireballs also explode on impact, or would they cancel each other out? Would it result in a smaller area of higher energy than each individual fireball? A larger area of the same energy? I'm having a hard time imagining the reaction, as there is no noticeable kinetic energy in said fireballs, at least to my knowledge.
To aid in consistency, I like to pose magic systems as sort of a 'vague physics', which allows rules to be defined that lead to guiding how things interact.
As the fireball magic manifests in your setting's reality, what form does it take?
- Is it a 'pure energy' that react as it touches some solid matter? Then maybe treat them as 'waves', in that they will pass through each other, but greatly amplify at the point of intersection. [and woe to any matter that 'sets them off' when that happens.]
- Does it manifest as something more gaseous or physical in nature? In which case they may act more like two water balloons hitting each other, or maybe like vortexes colliding. [Maybe check out the youtube channel "Smarter Every Day" for examples to take inspiration from?]
- Is magic unstable in nature and relies on some manner of 'confinement energy' for a spell's energy to continue? Maybe spells hitting each other can cause them to simply fizzle out because their confinement fields smash into each other, collapsing the spell.
The ranges of possibilities is rather large, and hopefully others can add more examples here, or with other answers.
The rules can be as flexible as you wish to define them, and tailored to your needs. - If you're writing, you may not need to have overly hard and fast rules, or may simply refer back to "What happened last time I wrote this" and ask yourself if that seems consistent. - If you're designing a game system or something, then you'll probably want more formality in how you define things. Or just keep them simple with things like "Apply the effects of both, and don't bother interacting".
Whether they explode in impact is entirely up to you and your rules of magic, it is entirely based on what holds your compressed plasma together. If they do we know what they will look like.
A chaotic state of charged particles is called a plasma, we have experience with how plasmas interact with each other and it is largely based on whether it has a charge. I will assume your fireballs do not have a charge because otherwise it is more electricity/lightning than fire.
The only thing you really have to decide is whether the explosion is supersonic or subsonic, supersonic explosions have a blastwave, subsonic do not. But really the interactions are similar enough. Anything with mass has inertia and thus can push against other things with eneria, two balls of uncharged plasma meeting will be much the same as two balls of gas meeting, if they have roughly equal inertia they splash outwards. They basically bounce off each other. Mythbusters even did a great program showing how two explosions interact.
If you want to visualize what it looks like I suggest you look at vortex collisions.
Explosive blastwave collisions are already well studied and in practice it is similar to how vortexes work just with far more energy and more back bounce.
It is magic so it is hard to say since nobody knows or explains the inner workings of a fireball.
You could think of all the spells made out of some energy that exists in fantasy worlds, maybe to simply think about water. You can throw it super hot, you can make steam out of it, make it solid so is this magic energy, but with more variations and less laws of physics.
I guess if you really want to attribute logic to magic, you could think about two water balloons in real life thrown at each other and just assume they work the same way, but instead of water it is the magic energy that collides. That is the most logic explanation to a fireball that I can think of.