The original religious community founded by Buddha has many descendents.
Each descendent is called a "school." The separate "schools" in Buddhism are like the separate "churches" in Christianity, such as the Greek Orthodox Church, the Roman Catholic Church, the Lutheran Church, etc.
We will cover here the major schools which developed between the years 500 and 100 BCE.
Buddhism as an organized religion remained united from the time of death of the Buddha, roughly about 500 BCE, until some time roughly between 350 BCE and 290 BCE.
At that latter time, the community of all Buddhists split up into two groups or "schools" over differences of opinion concerning what exactly were the true teachings of the Buddha in certain areas of monastic discipline. This event is called the "Great Schism" by some modern historians of Buddhism.
One of these two schools is called the Sthaviravada. The other school is called the Mahasanghikha. From these two branches of Buddhism, many limbs grew.
Sthavarivada means, in Sanskrit language, "The Teaching of the Elders." The Sthavarivadins claimed that the Mahasanghikins had changed the original rules of conduct for Buddhist monks and nuns established by the Buddha himself.
By 230 BCE, the Sthavarivada School was continuing on mainly as the Vibhajyavada School. Other off-shoots of the original Sthavarivada School at that time included the Mahisasaka School and the more radical Vatsiputriya (Pudgalavada) School.
Members of the still extant Theravada School of Buddhism claim that their school is a direct, unbroken continuation of the original Sthavarivada school and that they fully maintain the original orthodoxy. (Theravada means "The Teaching of the Elders " in Pali language.) They consider their tradition to be the same as their predecessors in their lineage. Thus they say that the true Sthaviravadins and the true Vibhajyavadins actually were Theravadins, and that they themselves are simultaneously true Sthaviravadins and true Vibhajyavadins.
Mahasanghika literally means "The Great[er] Community." The Mahasanghikins claimed that the Sthaviravadins had added inventions of their own to the original rules of conduct taught by Buddha. They also had some differences in regard to Buddhist doctrine. But these seem to have been less of a matter for contention at the time of the actual schism. They may even have arisen later.
Roughly around 270 BCE, a group splintered off from the main body of the Mahasanghkin School and became the Caityavada School. The Caityavada School eventually broke up into the Aparasaila School and the Uparasaila School.
By about 230 BCE, the remaining body of the Mahasanghika School had split into the Golulaka School and the Ekavyaharika School.
The Golulaka School split around 210 BCE into the Prajnaptivada School and the Bahusrutiya School.
From the Ekavyaharika School, there eventually evolved the Lokottaravada School.