Design and build

Its just another phrase for a turnkey project particularly for multiple housing. County Councils for example employ that method at times.

For a one off house Im sure there are contractors out there who would provide the full service but it would be a foolish person that would go down that road.

They would design in accordance with the clients needs (whether that be Local Authority or whatever), which is then reviewed and agreed with the client, and then it goes through planning etc. Design still has to be in accordance with planning, development plan, building regulations etc.

It's basically the same as all projects except the designers (architects etc) work for (or in partnership with) the main contractor rather than the client. But the design still has to be done to suit the clients needs, approved/agreed with the client, and certified at the end. Though as muffler implies, when it comes to smaller projects like one-off houses the client essentially loses having their own representative and the contractor self-certifies their own work, which can be a messy situation where it goes wrong.

I'd also add, for larger jobs like Local Authority works etc, the Local Authority would likely have their own Clerk of Works or other representatives periodically visiting the site and issuing reports following their inspections, to detail progress and any issues identified. So although it's essentially self-certification on the side of the contractor D&B group, there would still be oversight and representatives from the client side reviewing and inspecting the works (which again, is what you would lose in a private one-off house or extension with a design & build contractor).

The contractor doesn't have free reign. They are rarely designing from scratch. It's easier if you think about it as they are finishing off the design.

A traditional contract is where architects and engineers design and document the works in full to 100% and its given to a contractor. Everything less, where the contractor has to complete an element of the design is a Design and Build/Construct.

A common type is the project is tendered as ~75% complete, and the contractor completes the last 25%. The vast majority of commercial projects I work on are like that.
But they could be contracted at 50%, 30% or whatever. With lower %, the design tends to be more conceptual with minimum requirements built into the contract.