Integers can be considered “whole” numbers - the span of discrete “countable” numbers from negative to 0 to positive. For example, -134, 0, and 175 are integers. What that linked article on Number says is that JavaScript doesn’t actually store these numbers as integers though. Other languages have an integer type, like C++ and Java for example, but JS converts these numbers to a floating point format instead.
Real numbers include all the numbers that might or might not have decimals. Integers are a subset of that, and are numbers that don’t have decimals.