This article clearly differentiates between the two materials veneer and plywood.
Wood Veneers are very thin slices of wood obtained from logs of trees. The most common method of obtaining veneers is by mounting the logs on a machine and rotating them about their longitudinal axis while a cutter peels off layers from the logs. These peeled layers are called veneers. The other method for obtaining veneers is slice-cutting instead of rotary-cutting, and it produces veneers of an even better quality.
Decorative veneers of high quality are usually obtained from trees such as oak, mahogany, maple, walnut, cherry or from teak wood.
These thin slices of wood (veneers) are usually glued over lesser quality wood surfaces to increase their beauty and richness. e.g. decorative Teak veneered plywood would mean a veneer of teak wood glued over a cheaper plywood surface. Doing this achieves the effect of getting a surface finish of teak, while the total cost of the furniture remains under control because the plywood underneath is of a lower cost. In comparison completely solid teak wood will cost several times more.
Plywood construction also involves the same methodology as described above. Veneers are obtained from good quality timber logs, and these veneers (a minimum of three) are then stacked upon one another and firmly glued together using adhesives such as urea melamine formaldehyde resins or synthetic phenolic resins, and by hot-pressing them together under high pressure.
Also while stacking the layers (veneers) upon one another, care is taken that the grain pattern alternates in each adjacent layers. This is what makes plywood such a strong material.
Decorative Veneered MDF:
In the construction of kitchen cabinets, the cabinet shutters are often made from veneered MDF material. What this means is that the base wood or substrate over which the veneer is glued, is not plywood. It is MDF (Medium density fibre board). The decorative veneer glued over the MDF surface can either be a high-quality natural wood veneer, or it can be an artificial veneer.
MDF boards are made from very fine particles of wood, called wood fibres. Glue is mixed with these particles, and the mixture is firmly compressed together to make these boards. MDF is slightly cheaper than good quality plywood.
Alternatives to veneer?
Amongst the top alternative to using costly wood veneers, is to laminate the wooden surfaces with a decorative laminate. High pressure decorative laminates (such as Sunmica, Formica and other brands) are made from paper soaked in plastic resins. A printed decorative paper soaked and saturated with transparent melamine resin is pressed over a brown craft paper soaked in synthetic phenolic resin, to make these laminates.
Laminates are hard, water-proof, scratch-resistant, and easy to clean and maintain. Natural wood veneers on the other hand have to be polished from time to time.
Decorative laminates are available in several varieties such as plain solid colours, or high gloss ones, and also those that resemble the look of all the natural wood surfaces.