Wikipedia has this interesting chart:
Old Side vs. New Side:
Schism in American Presbyterian church from 1741 - 1758, controversy surrounding the First Great Awakening. Also known as the Old and New Light (including Congregationalists and Baptists) debate: When denomination splits into two: Old Lights = conservatives who do not wish changes, New Lights (George Whitefield, Jonathan Edwards, Gilbert Tennent, etc.) = those who prefer the changes. The Great Awakening calls for true conversion via preaching "terrors of the law". The Old side thinks that this type of faith policing has gone too far.
Old School vs. New School:
Schism in American Presbyterian Church in 1837, lasted 20+ years.
Old School, led by Charles Hodge of Princeton Theological Seminary, conservative, did not support the the 2nd Great Awakening.