The soda bread sandwich is named for its bread because the bread is the part that decides everything else. Irish soda bread is raised with bicarbonate of soda and buttermilk rather than yeast, which gives it a dense, tender, slightly cakey crumb, a faint sour tang from the buttermilk, and a thick, hard crust where the loaf has caramelised in the oven. It does not behave like a soft floured roll or a sliced white loaf: it is sturdier, drier, and more flavoured, and a sandwich built on it reads as soda bread before it reads as whatever is inside. The loaf is the lead here, and the form follows from a bread that has staling built into its chemistry.
The craft is governed by what soda bread does and does not do. It has no gluten development to speak of, so it goes stale fast: it is at its best the day it is baked and is filled and eaten the same day rather than packed ahead, which is the central scheduling fact of the form. Cut thick it is dry and crumbly and overwhelms a delicate filling, so it is sliced moderately and buttered firm to the edges, the butter doing structural work against a crumb that drinks moisture and against a filling that would otherwise dry against it. The dense crumb is a moisture advantage with a wet or fatty filling, which it holds without collapsing the way an open white crumb would, and the bread's own sour edge means it suits assertive fillings, smoked fish, a sharp cheese, ham and pickle, that can answer it rather than be lost against it.
The variations are mostly a question of what the loaf carries and how it is cut. Brown soda bread, made with wholemeal, pushes the nuttiness and density further; a fruit soda is a sweeter loaf for jam or butter; the soda farl, the same dough cooked flat on a griddle into a soft quarter round, is the close griddled cousin that behaves differently enough to stand apart. The smoked-fish and the ham-and-pickle builds are the fillings the loaf most often carries. Each deserves its own article rather than being crowded in here.