Between Hutton's day and Lyell's there arose a new geological controversy, which largely superseded, but is often confused with, the old Neptunian-Plutonian dispute. The new battle became an argument between catastrophism and uniformitarianism—unattractive terms for an important and very long-running dispute.
Catastrophists, as you might expect from the name, believed that the Earth was shaped by abrupt cataclysmic events—floods principally, which is why catastrophism and neptunism are often wrongly bundled together. Catastrophism was particularly comforting to clerics like Buckland because it allowed them to incorporate the biblical flood of Noah into serious scientific discussions. Uniformitarians by contrast believed that changes on Earth were gradual and that nearly all Earth processes happened slowly, over immense spans of time. Hutton was much more the father of the notion than Lyell, but it was Lyell most people read, and so he became in most people's minds, then and now, the father of modern geological thought.
Lyell believed that the Earth's shifts were uniform and steady—that everything that had ever happened in the past could be explained by events still going on today. Lyell and his adherents didn't just disdain catastrophism, they detested it. Catastrophists believed that extinctions were part of a series in which animals were repeatedly wiped out and replaced with new sets—a belief that the naturalist T. H. Huxley mockingly likened to "a succession of rubbers of whist, at the end of which the players upset the table and called for a new pack." It was too convenient a way to explain the unknown. "Never was there a dogma more calculated to foster indolence, and to blunt the keen edge of curiosity," sniffed Lyell.