No, they are not the same, and the difference is not a technicality. One answers when somebody is hurt or something is damaged. The other answers when the only thing lost is money. A single test separates almost every real case, and getting it wrong means buying the wrong half of what a client asked for.
The test
Was there physical injury to a person or damage to property belonging to somebody else. If yes, public liability. If the only loss is financial and it flowed from your work or advice, professional indemnity. A visitor tripping over your cable is the first. A client losing money because your report was wrong is the second.
They also behave differently
Public liability responds to events that occur during the policy period. Professional indemnity responds to claims first made during it, whatever year the work was done. That is why a professional indemnity policy has to be kept continuous long after a project ends and a public liability policy can be allowed to lapse when the activity stops.
A worked example, because the words are abstract
A consultant is engaged to recommend a system. The recommendation is made without checking a constraint the brief named, the client buys and implements it, and eighteen months later has to replace it. Nobody was injured, nothing was broken, and the client is several hundred thousand pounds down. The claim is for that loss and for the cost of arguing about whether the constraint was really in the brief, and both of those are what professional indemnity pays.
Questions people ask about is professional indemnity insurance the same as public liability
Are they the same thing?
No. Public liability covers physical injury and property damage to third parties; professional indemnity covers pure financial loss from your work.
Can one policy include both?
Yes, as sections of one business policy, which is how most UK insurers sell them and what most clients want to see on one certificate.
Which do I need?
Public liability if your work happens where other people are; professional indemnity if anybody relies on your work. Most businesses are both.