Of course, if you want the sweetness of Cool Whip but don't have any on hand, you can also make your own by whipping standard heavy cream with powdered sugar and vanilla. That's not to say you should ...
Is heavy cream the same as heavy whipping ... stiff peaks to lumpy and unappealing very fast. If you over-whip the cream too far, it can even turn into butter. You can fix over-whipped cream ...