The arrangement in plain terms
The vendor builds and runs the software: the ledger, bank connections, categorisation, invoicing and reporting. The firm licenses the right to present that software as its own, supplying a name, logo, colours and templates. Clients experience the firm’s product. Behind the scenes, updates and hosting remain the vendor’s job, so the firm does not become a software company.
This differs from simply recommending software. When you recommend a product, the client signs up with the vendor directly and the vendor’s brand sits between you and them. Under a white-label license, the firm is the face of the tool, and the vendor usually stays in the background of the client’s day-to-day experience.