AS3 What is a static class?

programming flash
1

I was wandering whether is it required that all the functions and variables must be static in order to be a static class. Like Math.random()

Or having 1 function or variable in a class is static makes it as “static class”?

Edit:
And which way is correct to write this?

public static function AyumiloveAS3():void {}
static public function AyumiloveAS2():void{}

var public static ayuTemp1:int = 0;
var static public ayuTemp2:int = 0;