Stable pyramid
A population pyramid showing an unchanging pattern of fertility and mortality.
Stationary pyramid
A population pyramid typical of countries with low fertility and low mortality, very similar to a constrictive pyramid.
Expansive pyramid
A population pyramid that is very wide at the base, indicating high birth and death rates.
Constrictive pyramid
A population pyramid that comes in at the bottom. The population is generally older on average, as the country has long life expectancy, a low death rate, but also a low birth rate. This pyramid is becoming more common, especially when immigrants are factored out, and is a typical pattern for a very developed country, a high level of education, easy access to and incentive to use birth control, good health care, and few negative environmental factors.
In some countries the above "pyramids" are referred to by a description of their shape. The classic one is of course the pyramid. The stationary pyramid is referred to as a "clock-model" (like the bell in a clock tower). The contracting pyramid is referred to as "onion" shaped. Sometimes even as "urn" shaped.