Everybody's dancin' around it but it doesn't sound like anybody's nailed it. Here's my attempt: Smoke production is all about oxygen, as many an old boy scout can confirm (assuming that new boy scouts can't play with fire these days because it's too dangerous). Smoke wood smolders in the WSM, making lots of smoke from a small piece, because you have the oxygen source choked down to the point the piece will not ignite. You are actually making charcoal out of your smoke wood.
This is why you need to put chips in a foil packet to make them smoke. Chips are much easier to ignite because of the increased surface area. Foil excludes the small amount of oxygen in the WSM, making a micro-environment of even lower oxygen, which prevents flaming the chips.
I've never used a stick burner, but if you are going to generate any significant heat with wood you must be giving it lots more oxygen than in the WSM with charcoal. Some smoke will be generated as well, but proportionately less.