Flat Slab:
A flat slab is a slab with no drop beams. As the name sounds, think of it as a sheet of concrete, extending in all directions and supported on columns. That's it.
In cases where the design loads are high, flat slabs will have drop panels at the columns. This panel thickens the slab at the support point [column] and resists what we call 'punching shear.'
Flat slabs without drop panels are quite common and are referred to as 'Flat Plates'. It is an excellent structural practice to have drop beams at the edge of the slab only – usually the exterior of the building.
Solid Slab :
Now for the solid slab; this is a typical slab that is used in traditional design, it is typically, a slab surrounded by drop beams. Solid slabs are less expensive because they require less thickness - however, they are not a favoured solution by architects since the drop beams stand in the way of creating a vast open space.