An employment agency is one that provides staff who is then employed by the client employer.
An employment business on the other hand, provides staffs who do not become employed by the hirer but who are seconded or supplied to a client employer.
So an employment business pays their staff directly, whereas an employment agency simply finds staff and passes them onto an employer who deals solely with their remuneration.
There’s more to it than this though – neither can demand exclusivity, neither can charge for finding work (or insist that you use other paid services – and plenty more. Read the whole thing here.