I am projecting here, perhaps, but I think the question you're asking is "why doesn't my salmon come out moist and succulent like what I get at the store?"
A couple reasons.
First: you want to properly cure the salmon for at least 24 hours beforehand. 36 is better. To cure, you will need two whole sides of salmon (or one cut in half), with the skin on. Rub your cure into the flesh--so 2:1 salt:sugar, plus whatever other spices you care to use. The addition of brandy sounds lovely; I like tequila or a nice peaty/smoky Scotch myself, or maple syrup (but obviously nix the sugar if you're doing that). Place the two pieces together, flesh to flesh, optionally including herbs between. Wrap very tightly in plastic, completely sealed, bung into your fridge to let it cure.
Second: when the fish is cured, remove from the wrap, rinse off the cure.
Third: time to smoke. If you want dry and flaky, hot smoke--this seems to be what you're doing and what you don't like. Therefore, it's cold smoke time. The two basic ways to do this are either to add LOTS of trays of ice to the smoker itself, or to route the smoke through a cooler filled with ice and then back into your smoking chamber. A quick Google should provide you with diagrams for doing so.
Do not over-smoke. Fish picks up flavours quite readily, and will dry out if oversmoked, even if cold. Really for salmon I don't think you need much more than 20 minutes of cold smoke.
You can use a gas grill for smoking and indirect cooking. Run the burner on one side of the grill, and place the food on the other. Wrap wood chips in foil, poke a few holes in it, and place the foil pack over the active burner. You can soak the chips if you like. I've never seen much point in that, myself. The water evaporates rather quickly, and you're back with dry chips. Better to limit the oxygen supply to the wood so it will smolder, and place the smoke pack somewhere so that it does not have too much heat applied to it.
It absolutely does matter what kind of wood you use. Avoid soft and sap-laden woods like pine. Stick with hardwoods or fruit woods. Hickory is often paired with pork. Apple and cherry are used ubiquitously. Oak is strong, but imparts an interesting flavor. Mesquite can be too powerful for some people -- I personally use it for grilling, but never for smoking.
Finally, be aware that you are going to have some limitations with your gas grill. It neither holds nor convects heat in the same manner that purpose-built smokers and some charcoal grills do. You are more likely to have hot and cold spots on your grill, so you will need to examine what you are cooking each hour and adjust accordingly if necessary. You will also not get nearly as much smoke to your food, so you will also have to adjust how much wood you use accordingly (though many people make the mistake of too much smoke in their barbecue, so a gas grill's limitation in this regard can be a benefit).
Best Answer
No, it won't be different. It is, however, a bit harder.
The issues are mainly:
That said, I smoked for years on a Webber grill, and it worked just fine. I did, however, upgrade to a Big Green Egg at the first available opportunity. The results are more consistent and the process is much easier. But you'll be fine getting started with the webber.