Solid Koa moulding is, as the name implies, a solid piece of Koa wood that is shaped to a given profile.

Veneer Koa moulding is a thin layer of Koa wood that is applied over a less expensive, shaped substrata.  This helps reduce the cost and "stretches" the supply of Koa available for mouldings.

It does not mean that the moulding is a "cheap" imitation.  The use of wood veneers has been a long time practice in the moulding industry; making exotic woods more available and less expensive.  

When the frame is completed anybody, woodworkers included, would have a very hard time distinguishing the two.  Solid or veneer, when the frame is completed and on the wall, you only see the surface.