The panini is defined not by a filling but by a process, and in the British café it is the press that makes it what it is. A roll, usually a dense, slightly chewy oval with a close crumb, is filled, then clamped between two hot ridged plates that compress it, scorch grill lines into the crust, and drive heat through the middle until the bread crisps and the filling fuses into the bread rather than sitting loose inside it. That compression is the whole identity. The same roll with the same filling served cold is just a roll; run through the press it becomes a flatter, crisper, hotter object where the layers have welded into one. The format is the lead, and the filling is whatever the press is being asked to do that day.
The craft is heat against time and water. The plates have to be hot enough to crisp the crust before the centre is merely warm, but not so hot they scorch the bread over a filling that is still cold, which is the same patience problem a griddled toastie poses, solved under pressure. The bread matters more than in a cold sandwich: a close, firm crumb takes the compression and crisps, where an open, airy one would crush flat and go dense. Fillings are chosen for how they behave under heat and clamping force, things that melt, soften, or fuse rather than spill, because the press squeezes a wet or loose load straight out the open sides. The roll is filled to order and pressed at the point of sale, since a panini that has cooled after pressing goes leathery and loses the contrast between crisp shell and molten centre that was the entire point.
The variations are a question of what the press is fusing. The two café defaults, mozzarella with tomato and chicken with pesto, each lead on a different problem the heat creates and earn their own treatment. Ham and cheese, tuna melt, the Reuben-style and the sweet Nutella press all keep the same clamped-and-crisped logic with a different load. The toastie and the jaffle are close pressed-and-sealed relatives built on sliced bread rather than a roll. Each deserves its own article rather than being crowded in here.