How did republicanism and liberalism differ in eighteenth-century British North America?

In eighteenth-century thought (and nineteenth-century as well) liberalism had not necessarily a connection with the form of government one favored. For instance, Edmund Burke in all respects can be considered a liberal of his time in standing up for the rights of the American colonists, the rights of the Roman Catholics in Ireland, and for those of people in India who were mistreated in the early period of English colonizing during the administration of the East India Company governor Warren Hastings. It was only in his opposition later to the French Revolution that Burke came to be seen as the arch-conservative. But Burke had always been consistent in believing that monarchical governments, not republics, were appropriate for all the major European states. In spite of his sympathy and the pro-American speeches he delivered in Parliament, Burke had not wanted the Americans to break away and form a republican government, but to remain under the Crown if they were given the full rights of Englishmen.
Republicanism aimed at forming representative governments without a hereditary head of state or monarch. That the Americans were able to do this was largely seen in Europe, even by liberals, as an experiment that would fail. English Liberalism aimed at establishing and maintaining human rights within the long-standing framework of English democracy and freedom. The monarchy, of course, has been retained, but over the centuries different events going all the way back to the Magna Carta in 1215 have created and maintained the liberal traditions in England, later transferred to the U.S. and the rest of the Anglophone world.