Why two different types of milk. And, if allergic to milk,?

[Ms Bernie]

Old-Fashioned Banana Pudding

[duonyte]

If you are allergic to milk you probably could use almond milk or something else for the milk. This is a lactose-free sub for the sweetened condensed milk, Lactose-Free Condensed Milk Substitute

The two milks have different properties. The sweetened condensed contains the sugar for the recipe and also the milk is evaporated, so that it is richer than just plain milk. It will not break, and provides a creamy mouthfeel to a dish, much as would cream.

[Chicagoland Chef du Jour]

Milk is what is necessary to make pudding.
Sweetened condensed milk, is: A mixture of whole milk and 40% sugar, heated until 60% of the water evaporates, creating a sticky, sweet mixture.

If you are allergic to milk, find an alternative to milk (soy, almond, etc) or find a recipe w/o milk.
I am not sure what milk substitutes will give you the same result though.

[Zeldaz]

Super Simple Vegan Banana Pudding