The lemon curd sandwich is the made thing, two slices closed around the curd, and what defines it is that it is built to be sharp where most sweet sandwiches are only sweet. Lemon curd is a thick set spread of lemon juice, zest, sugar, butter, and egg yolk, sour before it is sweet, and putting a second slice on top changes the problem from how it tastes to how it behaves under a closed lid. Pressed between bread, the curd has nowhere to go but sideways, and because the butter and yolk in it keep it loose it will travel and bleed at the edges unless the build accounts for it. This is a closed sweet sandwich, soft and plain, and it lives or dies on a thin layer and a sealed crumb rather than on the curd alone.
The craft is the ratio and the press. Both faces of soft white bread are buttered to the edges before the curd goes on, because the butter waterproofs the crumb against a wet filling and its salt is what keeps the sweetness from going flat and lets the sourness lead. The curd is spread thin and kept back from the very edge, since a thick layer slides under the top slice and a flooded edge is the usual way this sandwich fails. The bread is pressed gently so the two faces hold the curd as one even band rather than letting it pool at one corner, then trimmed and cut, which is also why the crustless tea version exists: a crust resists a delicate filling and the whole point is that nothing should resist. Soft bread is not laziness here, it is the design, because chew would fight a filling that has no texture to push back with.
The variations are mostly about what is closed in alongside the curd. A thin layer of clotted or whipped cream slackens the acid into something closer to a dessert. A sharper berry jam beside it doubles the fruit and the tartness. The crustless finger-sandwich form is the same build trimmed for the tea tray. The other made sweet-spread sandwiches, marmalade with its bitter peel, the berry jams, run the same closed soft-bread logic on a different preserve. Each of those is its own build and deserves its own article rather than being crowded in here.