Leibniz had at one time, prior to Newton’s publication of his work, met Newton, discussed the concepts involved and, some say, saw preliminary notes. However, Newton’s calculus was concerned entirely with change with respect to time, since mechanics (laws of motion) were his principle interest. Some classical mechanics teachers and texts still use Newton’s “dot” notation where a variable with a single dot above it represents the first derivative of that variable with respect to time, two dots the second derivative, etc.
Leibniz, whose notation is commonly used today, considered change of one variable (dependent) with respect to another variable (independent). For instance, with pressure of an enclosed gas expressed as a function of temperature, the rate of change of pressure with respect to temperature could be determined at any point (with the usual provisos of continuity and continuous differentiability).
Leibniz was also very involved in philosophy/theology, having an ongoing discussion (through publication) with Spinoza. Experts have concluded that Newton and Leibniz invented (discovered) the calculus independently.