Presbyterianism has split more often and more formally than almost any other Protestant family, and the reason is structural: a body with courts, a written constitution and a right of appeal gives dissent a procedure to follow, and procedures produce documented separations rather than quiet drift.
In Scotland the pattern is unmistakable. The Secession of 1733 and the Relief Church of 1761 both turned on patronage, the right of a landowner to impose a minister on an unwilling congregation, which is a question of who governs rather than what is believed. The Disruption of 1843 was the same question at full scale: over four hundred ministers walked out of the General Assembly and gave up their stipends and manses to found the Free Church, and the immediate issue was whether the civil courts could compel a presbytery to induct a minister the people had rejected. Later unions put most of that back together, leaving several smaller bodies that did not join.
In the United States the splits ran along different lines. The Old Side and New Side divided in 1741 over revivalism and educated ministry; Old School and New School divided in 1837 over doctrine, mission agencies and slavery; the church divided North and South in 1861 and did not reunite until 1983. In 1936 a dispute over the theological direction of Princeton Seminary and the mission board produced the Orthodox Presbyterian Church; in 1973 the Presbyterian Church in America was formed by southern conservatives; and from 2012 a further body was formed by congregations leaving over ordination standards.
The tradition's own view of this record is divided between those who see fidelity and those who see a temperament, and both readings are argued from within it.