How did Gottfried Wilhelm Leibniz’s approach to calculus differ from Isaac Newton’s?

Gottfried Wilhelm Leibniz and Isaac Newton independently developed calculus, but their approaches differed significantly in conceptual foundation and notation.12

Conceptual Differences
* Newton’s Fluxions: Newton viewed variables as "fluents"—magnitudes that flow over time—and defined their rates of change as "fluxions," denoted by a dot over the variable. His early work focused on infinite series and power series, later shifting toward a geometric theory of limits in his Principia to avoid analytic processes.21
* Leibniz’s Infinitesimals: Leibniz treated continuous quantities as if they were discrete. He defined the derivative as a quotient of infinitesimals—infinitely small increases in variables—and viewed the integral as a sum of these infinitesimal strips.1

Notation and Influence
Leibniz’s primary contribution was the development of a powerful, general algorithm using the symbols $d$ for differences and $\int$ for sums. This notation proved superior for solving complex problems and became the standard for modern calculus, whereas Newton’s geometric approach and fluxion notation were less influential in the long term, contributing to the relative isolation of British mathematics in the 18th century.12