Personal injury cases are civil cases. A personal injury lawsuit seeks to assign fault to another party and make that party pay money to the victim.
Some criminal and personal injury cases can overlap (for example, a drunk driver hits another vehicle and causes severe injuries; they will be tried criminally first, but they can also be tried civilly).
Several types of cases can fall under the “personal injury” umbrella:
motor vehicle accidents
public transportation accidents
slip and fall accidents
dog bite accidents
defective products
and many more