Examples of invert sugars are honey, glucose, corn syrup, and trimoline. You can't make it at home because no home processor will grind it to that powdery texture. It is used to sweeten because it dissolves more easily than granulated sugar. It is also used to thicken because it usually contains cornstarch. I usually use light brown sugar, but for Creme Brulee it doesn't matter.
Brown sugar is a mixture of granulated sugar and molasses.
You can substitute brown sugar for granulated sugar any time the flavor of the recipe will not be altered by a slight taste of molasses. This is starch extracted from corn kernels and treated with an acid or enzyme to create a sweet syrup. Its presence will keep sugars from crystallizing. Corn syrup is an invert sugar, meaning it takes half as much of it to sweeten as much as regular sugar. Corn syrup helps baked good retain their moisture and increases shelf life.