The condensed milk sandwich is the sweet thrift sandwich at its most extreme, and its entire logic is the behaviour of a sticky spread. Sweetened condensed milk is cow's milk reduced with sugar to a thick, pale, intensely sweet paste that pours slowly and sets tacky. Spread on buttered bread and closed, that is the whole sandwich: no second component, no fruit, no technique. The defining fact is that the filling is one concentrated sweetness with the consistency of soft caramel, and the sandwich exists because a spoonful of something that sweet and that cheap can turn plain bread and butter into a treat when there is nothing else in the house.
The craft, such as it is, is the butter and the ratio. Butter is structural here rather than flavour: it waterproofs the crumb so the milk does not soak straight through, and its salt is the only thing stopping the sweetness reading as flat and cloying. The condensed milk is spread thin, because it is heavy and tacky and a thick layer slides out the sides under the slightest press and overwhelms the bread entirely. The bread is soft and plain because chew would fight a filling with no texture of its own, and the sandwich is closed and pressed gently so the sticky layer grips both faces and holds rather than oozing. There is no contrast being managed here the way a savoury sandwich manages it; the pleasure is the single deliberate hit of plain bread, salted butter, and a near-toffee sweetness.
The variations stay inside the sweet, soft, single-anchor frame. A scrape of jam or mashed banana under the milk adds fruit but keeps the sticky-spread logic. Golden syrup or treacle is the same idea with a different concentrated sweetness, thinner and darker. Condensed milk on its own without even the butter is the form stripped to one ingredient. Each of those is its own sandwich and deserves its own article rather than being crowded in here.