Short answers, pulled from the story.
Nikaya Buddhism is a scholarly term for the early Buddhist schools that predate the Mahayana movement. These schools were organized as monastic fraternities in India, conventionally numbering eighteen, each with its own doctrinal orientation and scriptural canon.
Masatoshi Nagatomi of Harvard University coined the term "Nikaya Buddhism." According to Robert Thurman, Nagatomi created it to avoid the pejorative connotations of "Hinayana," the older label meaning "inferior vehicle."
Nikaya Buddhism conventionally encompasses eighteen schools, though the actual count varied across time and region. Each school maintained its own scriptural canon organized into collections called pitakas, and the number and content of these collections differed from school to school.
Mahayana Buddhism never formed a separate formal school or established its own ordination lineage apart from the Nikaya fraternities, according to scholars Jan Nattier and Paul Williams. Every Mahayana monk and nun formally belonged to one of the Nikaya schools. This arrangement continues today through the Dharmaguptaka nikaya in East Asia and the Mulasarvastivada nikaya in Tibetan Buddhism.
"Hinayana," meaning "inferior vehicle," was coined by the Mahayana tradition and was never used by the early Buddhist schools themselves to describe their own practices. The Tibetan Buddhist scholar Reginald Ray described the term as "a stereotype" whose technical meaning within Tibetan philosophy does not accurately characterize living historical schools like the Theravada.
Theravada Buddhism, which follows teachings preserved in the Pali Canon, is the living tradition most closely identified with the Nikaya schools. The Dharmaguptaka nikaya remains active as the ordination lineage for Mahayana monks and nuns in East Asia, and the Mulasarvastivada nikaya serves the same function in Tibetan Buddhism.