By definition, a constellation is a group of stars forming a recognizable pattern that is traditionally named after its apparent form or identified with a mythological figure.
A star pattern that is not officially recognized by the international scientific community as a constellation is called an asterism.
The stars that form asterisms can be part of one or more constellations.
For example, the Big Dipper is an asterism within the Ursa Major constellation.
The Square of Pegasus, on the other hand, is an asterism made up of three stars from the Pegasus constellation and one star from the neighboring Andromeda constellation.
Greek astronomers were the first to formally identify and list 48 constellations (often referred to as the traditional greek constellations) in 2nd century texts by Aratus (Phenomena) and Ptolemy (Almagest). Of course, listed were only the constellations visible to them, from their earthly viewpoint - ie the Northern Hemisphere. These were the first written and scientific accounts of the constellations and were used for centuries as the benchmark for astronomy. The identification and listing of Southern Hemisphere constellations began only in the 15th century when European explorers began traveling to the Southern Hemisphere. The likes of Petrus Plancius, Johannes Hevelius, and Nicolas Louis de Lacaille contributed most of what we now know about the southern skies.
In 1928, the International Astronomical Union formally divided the sky into 88 official constellations. Of the 88 modern constellations, 36 lie predominantly in the northern sky, and the other 52 predominantly in the southern sky.