Essentially this boils down to when a decision is made to limit the products offered to clients. For an independent service, the decision is made after the adviser meets the client, essentially excluding products and services that don't meet the client's requirements and selecting solutions that remain from the whole retail market. With a restricted firm, this decision is made before the adviser meets the client, excluding one or more products or services from being used with any clients.
In the most restrictive form, a firm may be limited to only distributing the products offered by their company. This is often termed "vertical integration", and it can ultimately look a lot like pre-Retail Distribution Review distribution channels, including remuneration structures that bear an uncanny resemblance to commission, which is generally banned on investments and pensions.
Importantly, all advice is subject to the same regulations and requirements. As such, regardless of whether an adviser is restricted or independent, they must first carry out a fact-finding exercise, identify goals, assess the client's risk profile, then advise on a suitable solution given everything they have learned.