Personal injury is an area of law that covers when someone is hurt by the actions of another, typically as a result of an accident. The "actions of another" in this area is usually negligence, which can be thought of as the failure to do what you're supposed to do. There are a ton of examples. Take a car accident, for instance:
Now negligence doesn't mean that someone is a bad person - accidents happen. But that leaves little comfort for those who are left with an injury. That's why the law provides a legal remedy for this exact sort of thing.
Personal injury law (the law school word is "tort" law) allows an injured person to file a lawsuit in court to recover damages caused by an accident. This is a civil lawsuit (aka between private persons or companies) as opposed to a criminal lawsuit, which is prosecuted by the State. The idea of a personal injury lawsuit is to get the injured person back to their pre-accident condition by financial compensation and made whole again.
Sometimes though, the injury is serious enough that the person will likely never be back to their pre-accident self. Again the personal injury system steps in to allow these victims compensation for not only damages they've suffered in the past, but also damages for what they may experience in the future. See below.
Personal injury claims come up in countless scenarios, like a car accident, truck accident, 18-wheeler wreck, slip and fall, offshore injury, dog bite, medical malpractice incident, wrongful death claim, motorcycle accident, pedestrian accident, and many others, like premise liability and defective products. Essentially, if you're injured and it wasn't your fault, you most likely have a personal injury claim.
The biggest factor on a personal injury claim, aside from the extent of the injury, is the ability of the wrongdoer to pay for the claim. Most people can't afford to pay out of pocket - that's why insurance is so important.
It's confusing. We get it. Here's the down and dirty.
The term claim is initially used to describe a request made on the insurance company for policy coverage, whether for bodily injury, property damage, etc. You don't need a law degree or any technical knowledge to make a claim against an insurance policy.
The term case is used to describe a legal lawsuit filed in a court of law. There a lot types of cases. It could be personal injury case, a breach of contract case, employment case, etc. A case is also comprised of "claims" (unrelated to insurance claims) that represent the assertions and demands made on the other party. You need a law degree to file a lawsuit and pursue a case in court.
In the world of personal injury, there are two options: (1) make a claim first, or (2) file a case first. The decision depends on the facts and best strategy for each client. Typically, you have a claim with the insurance company for your damages. If the insurance company denies the claim or doesn't offer enough, the claim turns into a case to be determined by a jury.