It Makes Sense
Generally, when making a sandwich, you would get two slices of bread and your chosen fillings.
A smaller sandwich made with one piece of bread folded in half down the middle can be called many names, such as a pocket sandwich. If you’re simply looking for a snack, this will suffice. His family most likely called it by a more distinct name since they realized that not everyone would understand what they meant if they said “pocket sandwich.”