The banana sandwich is a sandwich with a clock running against it. Banana flesh browns and softens the moment it is cut, so the plain build, mashed or sliced banana on buttered white bread, is at its sharpest in the few minutes between assembly and eating and noticeably worse an hour later. This is the defining fact of the form. It is a childhood sandwich and a made-to-order sandwich by necessity, not by ceremony, and any version that has to survive a lunchbox is fighting the fruit's own chemistry.
The craft is almost entirely about that oxidation and the moisture it brings. Mashed banana spreads and binds but bleeds faster and goes grey sooner; sliced banana holds its shape longer but slides under the top slice and makes the sandwich hard to bite cleanly. Butter spread to the edges is structural rather than incidental: it waterproofs the crumb against a filling that is mostly water and slows the bread going to a damp paste from underneath. Salted butter does a second job, because banana on its own is flat-sweet and the salt is what stops it reading as bland. The bread is soft and plain on purpose, since a banana with no texture of its own gains nothing from a crust with chew and only suffers from one that fights it.
The variations are mostly attempts to fix the timing problem or to add the contrast the plain version lacks. Sugar sprinkled on the banana adds grit and a faint crunch and is the most common British addition. Honey binds and sweetens but adds moisture the bread has to absorb. Peanut butter on the opposite slice slows the browning a little and supplies the salt and body the fruit does not have. Each deserves its own article rather than being crowded in here.