The question is pretty broad because greenhouses can be classified in a number of ways; by shape, structure or even by materials. Greenhouses are designed based on regional weather patterns as well as the type of plants to be grown.
To start from the basics there are three types of greenhouses. Gutter connected(ridge and furrow), contiguous and free standing(even span). Free standing is pretty self explanatory, they are not attached to another structure and the design is up to your imagination as long as you can find a manufacturer willing to make it. Gutter connected greenhouses are a series of houses connected at the gutter that do not have partitions separating houses and contiguous houses have the same design but with partitions. The illustration below clarifies the structural differences.
Within gutter connected and contiguous greenhouses there are many types of designs such as; arch gothic, open roof, A-frame, atrium, sawtooth, and venlo. Below is an illustration with common greenhouse designs.
Greenhouses can also be identified by the materials they are made out of. The primary materials used in the construction of greenhouses today are glass, poly and polycarbonate but fiberglass and acrylic are also available. Advances in polycarbonate has significantly improved the life as well as efficiency of greenhouses by offering excellent UV protection with an excellent R value. When deciding on which material to choose for construction you should consider lighting, insulating value, condensation, longevity and cost.
Some materials such as glass provide direct light which can be too much for some plants(many glass houses are sprayed with a coating to diffuse the light), while other materials like poly carbonate diffuse light.
Insulating value is another important consideration because heating costs are some of the biggest expenses growers face after labor and plant material costs. Having a well insulated greenhouse will hold in the heat during colder seasons lowering energy costs. An example of an improvement to insulating value is the idea of double poly. Some greenhouse are simply a frame with poly sheeting stretched over it. With the addition of another layer of poly, builders install a blower between layers so that an air pocket provides insulation improving efficiency.
Issues with longevity include UV degradation, material ripping (poly sheeting), rust and rot. Greenhouses are incredibly damp and humid because of plant transpiration and evaporation; this environment may be great for plants but is very hard on building materials over an extended period.
Another way to classify greenhouses could be by the systems used to control the growing environment.
There are two main heating systems; unit heater and boiler systems. Boiler systems have a variety of delivery options from fin tube under bench to bench top systems. There are also steam, infrared, and electrical resistance systems available but are not as common.
There are a variety of cooling systems such vent systems(ridge, pad, sidewall), pad and fan(evaporative cooling), swamp coolers(evaporative cooling), fan systems, AC units, and custom evaporative fan units.