They are not the same, and the difference is a single question: who was hurt. Everything else about the two covers, including why one is compulsory and the other is not, follows from that one distinction.
Who was hurt decides which policy answers
Employers' liability answers when a person who works for the business is injured or made ill by that work. Public liability answers when somebody outside the business is injured, or their property is damaged. A customer who slips is public liability. A member of staff who slips on the same floor is employers' liability. The two are never both responding to the same injured person, which is why a business needs both rather than choosing between them.
One is compulsory, the other is required
Employers' liability is compulsory by statute once a business employs anybody, with a certificate that has to be available to employees. Public liability is not compulsory for most businesses in the UK. In practice public liability is required by clients, landlords, trade bodies and venues so consistently that the legal distinction rarely changes what a business buys, but it does explain why one comes with a certificate regime and the other does not.
They are rated on different things
Employers' liability is rated on wage roll split by what people do, because the exposure follows the workforce. Public liability is rated on turnover, activities and where the work happens, because the exposure follows the work. That is why adding one member of staff moves one premium and taking on a larger contract moves the other, and why the two sections of a combined policy behave independently at renewal.
A combined policy keeps them separate inside
Most small business packages carry both sections, which is convenient and does not merge them. Each has its own limit of indemnity, its own conditions and its own claims. Employers' liability limits in the UK market sit well above the statutory minimum as standard, so a buyer rarely chooses that number, while the public liability limit is chosen constantly because clients name it in contracts.
Questions people ask about is employers liability the same as public liability
Is employers' liability the same as public liability?
No. Employers' liability covers injury to people who work for you; public liability covers injury and property damage to people outside the business.
Do I need both?
Employers' liability once you employ anybody, and public liability whenever your work touches people or property outside the business, which clients almost always require anyway.
Can one policy include both?
Yes, most business packages carry both sections, each with its own limit, conditions and claims.