The additional overloads are provided in this header (<cmath>) for the integral types: These overloads effectively cast x to a double before calculations (defined for T being any integral type).
The second sentence is just plain wrong.
If you include just <cmath> or <math.h> and call abs with an integer value, you will get an error message about an ambiguous function call. If you want to take the absolute value of an integer value, you need to include <cstdlib> or <stdlib.h>, whether or not you include <cmath> or <math.h> to get the floating-point versions.