1, different definitions: uniform convergence is an important concept in advanced mathematics, also known as uniform convergence. Convergence is related to interval (or point set) and has nothing to do with single point.

2. Different continuity: uniform convergence can keep the continuity of function sequence, but convergence can't. Among all kinds of convergence, convergence is the most intuitive and easy to imagine, but it can't keep some important properties of the function, such as continuity.