The terms Hinayana (theg-dman, lesser vehicle, modest vehicle) and Mahayana (theg-chen, greater vehicle, vast vehicle) appeared first in the Prajnaparamita Sutras (Sher-phyin mdo, Sutras on Far-Reaching Discriminating Awareness, Perfection of Wisdom Sutras) in approximately the 2nd century of the modern era. These sutras were among the earliest Mahayana texts and they used the two terms to assert that the scope and depth of their teachings far exceeded those of the preceding Buddhist schools.
Although the two terms carry sectarian connotations and appear exclusively in Mahayana texts, it is difficult to find adequate "politically correct" substitutes. "Hinayana" has become a collective term for eighteen Buddhist schools, only one of which is currently extant, Theravada. "Mahayana" similarly spans several schools. When the Indo-Tibetan tradition studies and discusses Hinayana systems of philosophical tenets, their reference is Vaibhashika and Sautrantika, which are Sarvastivada, another of the eighteen schools. Since some of the Hinayana schools appeared later than Mahayana, we cannot call Hinayana "Early Buddhism" or "Original Buddhism" and Mahayana "Later Buddhism."
Theravada is currently found in Sri Lanka and Southeast Asia. Dharmaguptaka, another of the eighteen Hinayana schools, spread to Central Asia and China. The Chinese monastic tradition follows the Dharmaguptaka version of the monastic rules of discipline (Skt. vinaya). Moreover, Mahayana spread to Indonesia, although it no longer survives there. Thus, calling Hinayana "Southern Buddhism" and Mahayana "Northern Buddhism" is also inadequate.
Both the Hinayana and Mahayana schools outline paths for shravakas (listeners to Buddha's teachings) and pratyekabuddhas (self-realizers) to reach the purified state of an arhat (liberated being), and for bodhisattvas to reach Buddhahood. Therefore, it is confusing to call Hinayana "Shravakayana" and Mahayana "Bodhisattvayana."
Consequently, although Theravada practitioners may find the terms Hinayana and Mahayana offensive, we shall reluctantly use them to refer to the classification of Buddhist schools, in face of the inaccuracy of the above-mentioned politically more correct terms.