The salmon burger is decided by how the patty is held together, because salmon does not want to be a patty at all. A beef burger binds itself: its fat and myosin knit into a coherent disc under heat. Salmon is lean and flaky and will fall to pieces on the spatula unless the cook builds structure into it deliberately. The Pacific Northwest version, where good salmon is the regional given, makes that binding problem the whole craft. Part of the fish is chopped coarse for texture and part is minced fine to act as the glue, bound with egg and a little breadcrumb or panko, so the patty holds its shape on the griddle while still reading as fish rather than paste. That tension, between enough bind to survive cooking and little enough to still taste like salmon, is the entire sandwich.
The craft is in the grind and the heat. Grinding all of the salmon smooth destroys the only texture it offers and produces a dense, springy puck; leaving it all in chunks gives a patty that disintegrates the moment it is flipped. The build splits the difference, and the binder is added with restraint because too much egg and crumb turns it into a fish cake that has lost the plot. The heat is moderate and the time short: salmon has no connective tissue to break down and little fat to render, so a patty left on the flat-top too long goes dry and chalky in the way an overcooked beef burger never quite does. The bun is the same engineering problem as a beef burger but with a leaner, more fragile cargo, often toasted on the cut face so a thin seared layer slows moisture from a sauce or slaw reaching the crumb. The standard counter is built for a clean protein rather than a fatty one: a dill or lemon mayonnaise, a caper or pickle note, a crisp slaw for the acid and crunch the fish itself does not bring.
The variations stay inside the formed-patty frame. A coarse-chopped build leans toward a seared salmon fillet held just barely together; a finer, smoother version is closer to a Pacific salmon cake on a bun. A teriyaki or miso-glazed reading pushes it toward the Japanese-influenced end of the Northwest, and the seared rare ahi build is the close cousin running a different fish through a different doneness. Each of those is its own preparation and deserves its own article rather than being crowded in here.