Bodily Injury Liability covers other people's bodily injuries or death for which you are responsible. It also provides for a legal defense if another party in the accident files a lawsuit against you. Claims for bodily injury may be for such things as medical bills, loss of income or pain and suffering. In the event of a serious accident, you want enough insurance to cover a judgment against you in a lawsuit, without jeopardizing your personal assets. Bodily injury liability covers injury to people, not your vehicle.
Property Damage Liability covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident. It also provides you with legal defense if another party files a lawsuit against you.
A split limit of $20,000/$40,000, would pay up to $20,000 for each individual and up to $40,000 for each accident.
CSL, or combined single limit, does not distinguish between individuals and accidents. A CSL of $100,000 would pay up to $100,000 for each accident with that going to as many persons as are affected.