I mostly agree with angryrainbow's response. I think I maybe place a little more importance on genetics when it comes to why some dogs become reactive and others don't.
To me, the big difference between reactivity and aggression is that a reactive dog is usually acting out of fear or annoyance, while the aggressive dog is dealing with an entirely different drive. An aggressive dog maybe sees that other dog as a threat, but it's more a "Hey, get off my turf!" type of threat than an actual fear. A reactive dog is acting out of (perceived) self-defense because he is honestly terrified of whatever it is that's setting him off, or he's so under-socialized that he can't tolerate normal behavior from other dogs.
It is important here to note that a major definition of "reactive" is basically "abnormal or excessive response." You can push pretty much any dog to react aggressively or fearfully in the right situations, so "reactive" is dependent on a dog's expected behavior in normal, non-threatening situations.
Also agreed that reactivity doesn't always manifest as aggression. A dog who cries and runs away in response to normal stimuli is just as reactive as the one who bites. True aggression, on the other hand, will never manifest as the dog running away or otherwise acting less than aggressively. Again, the aggressive dog isn't necessarily frightened in the traditional sense.
A reactive dog can absolutely be created, but some dogs are more prone to it than others. I have seen plenty of dogs attacked by others as puppies, who were not reactive afterwards. And then others are reactive to dogs without ever having had a bad experience.
I do think the one surefire way to create a reactive dog is a lack of socialization, but I think (based on my experience) that if you take a dog with a naturally strong temperament, lock him up in a crate and never let him see anything for the first 2 years of his life, and then start socializing him, it will go slower but you'll eventually get him over his reactive behavior.
Aggression is the same way. A truly dog-aggressive dog is born that way and will never get over it, although with training he may learn to tolerate other dogs to an extent. By the same token, training and experiences can help bring out the aggression in an otherwise friendly dog, but you can't create it in a totally submissive dog. Think of police dogs for this--they're obviously not killing machines, but a lot of dogs that wash out do so because they're not aggressive enough naturally.
Does your dog being attacked make it reactive ?
What makes a dog reactive is when the owner gets scared.
This is my main disagreement with angryrainbow (though the advice immediately following on how to handle the aftermath of a dog fight is great!).
I agree that this definitely happens--owners can easily make a bad situation into a much worse one by not handling it well! But I think that, short of avoiding all socialization afterwards, usually it is more dependent on the dog's natural temperament. If your dog is fearful and reactive by nature, he's going to respond worse to a bad situation, while a dog with a stronger temperament might just shrug it off no matter what the owner does.
In practice, though, it doesn't matter that much if your dog has a weak temperament or is just temporarily scared, because you deal with them the same way. You keep socializing the animal while being careful to not let them get over threshold and act out.
I also want to mention that minor dog fights (I usually refer to them as "squabbles" to differentiate them from serious "I'm going to kill you!" fights) aren't really a big deal. They happen when a puppy or a rude dog keeps pestering a dog with a normal temperament, or over food resources, etc. These fights look and sound scary, and may even occasionally result in minor injuries (scratches, once I saw a dog bite his own tongue, etc.) but aren't life-threatening and don't necessarily imply that either dog is aggressive or reactive. Normally the "attacked" dog will just get the picture and leave the winner alone.
Still they shouldn't be allowed/encouraged and management should be used to prevent them when dogs are together (separating the dogs if one is annoying the other, handling feeding time and treats in such a way that the dogs don't feel the need/have the chance to fight, etc.). If it happens too often, it can escalate or lead to other problems.