There is no general case but both cases exist. Some metal is inlaid within the ILD (inter level dielectric) while other metal makes up a via to another layer. This is one of the advantages of the dual damascene copper process, it reduces the number of process steps necessary and therefore improves cycle time. Nice overview
here.
In today's high speed logic devices signals are not routed to pads on the outside of the chip. The delay would be too great for the clockspeeds of today, therefore a process of attaching solder pads directly to the last metal layer is performed. The exact method used to form these connections is relatively proprietary.