Twins, but different fathers

I have actually heard real documented stories of twins being born to two different parents. It is rare, and I have no idea how it is possible but it is. I think the person would have most likely to have to have been with the same person as another within a very short time. I think I may have even heard of cases where one twin had entirely different features than another-such as one black one white-if the parents were both of different races.

So do they have the same blood type or not?

This is the first time I heard of such thing! That's weird.