The Welsh cake sandwich puts the cake itself in the lead. A Welsh cake is a flat, currant-studded round cooked on a bakestone or a heavy griddle rather than baked, so it comes off the iron with a faint crust, a soft crumbly centre, spice, dried fruit, and a dusting of sugar already on it. Split that round through the middle and butter the cut faces and the cake stops being a teatime biscuit and becomes the structure of a small sandwich. The defining fact is that the bread here is sweet, spiced, and short-textured before anything goes near it, so the build starts from a carrier that already tastes of something rather than a neutral slice waiting to be filled.
The craft is splitting and timing. A Welsh cake is best warm off the bakestone, when the inside is still soft and the sugar on the outside has not set hard, so it is split while it still has give and buttered straight away, letting cold butter melt just enough into the warm crumb to bind the two halves without making them greasy. The cake is fragile by design, raised with little more than the fat rubbed through the flour, so it is handled with a light touch and not pressed flat the way a bread sandwich would be, because pressure crumbles it rather than compacting it. Salted butter is the usual filling on its own, because the salt against the sugar and the currants is the whole contrast the sandwich is built on, and a heavier filling would only bury a cake that is already doing the work.
The variations stay inside the sweet, griddled frame. A smear of jam between the halves turns it toward a teatime treat; a thin layer of clotted cream pushes it richer; some cooks split a thicker bakestone round and treat it almost as a scone with butter and a fruit preserve. The closely related Welsh teabreads, Bara Brith chief among them, sliced and buttered, run the same logic with a yeasted fruit loaf instead of a griddle cake. Each deserves its own article rather than being crowded in here.