The difference is simple, and not very subtle; the Templars ceased to exist, and the Hospitallers certainly exist right now, working for the sick. Originally the latter were of a military order, the Knights Hospitallers of St. John of Jerusalem. The name comes from the dedication to St. John the Baptist of their headquarters in Jerusalem.
These are not their only names: from 1310 they were the Knights of Rhodes, and from 1530 the Knights of Malta, but they were established themselves first in (or around) 1070 with Muslim permission, managing a hospital for sick pilgrims in Jerusalem. They only became a formal order of knights when the city fell to the first Crusaders in 1099.
They wore a black habit, with a white eight-pointed Maltese Cross. They elected a Master and under him were at first purely military, in an order which spread quickly across Europe. In questions of order and discipline they followed Augustinian rules (q.v.) and divided themselves into three classes or ranks: knights, chaplains and serving brothers.
Driven out of Jerusalem by Saladin himself they moved to Acre, from which they were expelled a century later, transferring to Cyprus. In 1310, however, they captured the island of Rhodes and remained there until 1522. Then Emperor Charles V made them a present of the island of Malta, which they had to defend by force against the Turks, but they could not deal in a similar fashion with Napoleon: by this time the Order had lost its influence and supporting voices. (more…)