I had a brooklyn blackout cupcake which is a chocolate cake filled with chocolate pudding. Is this the same as a chocolate pastry cream?

I found this recipe by Gale Gand for a Brooklyn Blackout cake and here are the ingredients for the filling. I just googled Brooklyn Blackout Cake and got this:

Custard:
3 cups water
2 1/2 cups sugar
1 tablespoon corn syrup
1 1/2 cups unsweetened cocoa powder
Scant 2/3 cup cornstarch
6 tablespoons (3/4 stick) unsalted butter, cut into pieces
1/2 teaspoon pure vanilla extract

I am not sure if this is the same bakery that used to be in Park Slope Brooklyn, if it is i have had that same cupcake. The filling as i remember is not a traditional pastry cream. It was creamy but not heavy with milk or cream. It seemed to me to have water in it along with the milk making it a darker more intense chocolate. I could be way off and this is possibly a different bakery with a different recipe but that is my recollection.

Pudding can be very similar to pastry cream (which is typically made with eggs, flour, sugar and milk), but it really depends on the specific recipe used.