Would an american call that sausage in a bun from a truck a hotdog, or is it more of an actual sausage and not processed pink meatslurry?

In NZ we call the processed pink meatslurry in a bun an "American hot dog" because a "hot dog" here is a battered sausage on a stick (and now you are going to ask if that is what you would call a "corn dog" and I am going to say "kind of, but an American corn dog has much thicker batter")

It's a german wurst truck😁