Personal injury is a defined term, not a synonym
In an umbrella, personal injury generally means libel, slander, defamation, false arrest, malicious prosecution and invasion of privacy. It is a separate grant of cover from bodily injury. A strongly worded review of a contractor, or a post about a neighbor, can produce a claim in this category from a household that has never had an accident.
Not every umbrella includes it
Some policies include personal injury automatically, some offer it as an option and some exclude it. It is one of the real differences between umbrellas that otherwise look identical on price, and it is rarely what gets compared.
Defense is the practical benefit
Most defamation claims are defended rather than paid, and defending one is expensive. An umbrella that pays defense costs, often outside the limit, is doing the useful work long before any judgment exists.