The difference between a solid core and a braid stranded wire is that solid core wire is made from a single, thick strand of metal, whereas braid stranded wire is made from several smaller strands woven together. Each type has different uses. Primarily, the solid core wires are superior where toughness and keeping a shape is needed, whereas stranded wire has vastly superior flexibility.
A solid core wire is best for applications where minimal movement is needed, such as for circuits that are stable, and where bending is undesirable. Stranded wires are much more common, since flexibility is frequently needed. Stranded wire is better for very small circuits, where the wire may need to be strung around other components. Stranded wires are most commonly made with between 12 and 19 different strands of metal.
Wires are subject to a skin effect, where the electricity mostly travels along the outside surface of a strand. While the greater surface area of stranded wires is advantageous, in the end the gaps between the wires mean that a stranded wire of a given thickness carries less current than a similar solid core wire. This is only a minor disadvantage, however, and existing insulation technologies help compensate for it.