The casual cucumber sandwich is the same idea as the tea-tray finger with the ceremony stripped out, and the missing ceremony is what defines it. The crusts stay on. The slices are cut by eye rather than to translucence. It is built to be eaten standing at a worktop or handed across a kitchen, not arranged on a tiered stand, and that change of setting changes the whole sandwich. This is cucumber as an everyday filling rather than a delicacy: cool, plain, faintly green, made because there is a cucumber and a loaf in the house and that is enough for lunch.
The craft is still moisture control, but the tolerances are looser and that is the point. Cucumber is mostly water, so the slices want to be salted briefly and patted dry, but a casual build forgives a slice cut a little thick and a drain done quickly, where the formal version does not. Butter is spread to the edges to seal the crumb and supply the only seasoning the sandwich gets, and it works harder here because a thicker slice carries more water to hold back. The bread is soft white or a plain wholemeal, sliced normally and left whole with its crust, because the crust is no longer treated as an enemy of a delicate filling: this filling is not being protected, it is just being eaten. It still wants making close to when it is served, since cucumber goes limp on a wait whatever the occasion.
The variations are the everyday additions a tea sandwich would refuse on principle. A grind of black pepper or a little salad cream for a sharper edge; a slice of cheese or ham turning it from a light thing into a proper lunch; cream cheese instead of butter for a richer body. The crustless, paper-thin, finger-cut version is a different sandwich with a different brief, and that one along with each of these deserves its own article rather than being crowded in here.