* As crabjoe noted white and brown start as the same crystal sugar. The sugar will ferment out so that you have a slight residual sweetness. The grades of light to dark have increasing molasses added back (dirt & minerals) and this will change the flavor to the extent it does in making sweet rolls and switching from white to brown sugar, , , more rounded out flavor notes.
Table sugar is made from several plants as sugar beets and sugar cane. Since it is cleaned up there will be no difference in plant source.
* Fructose is readily available. It is very clean and would ferment out to alcohol therefore have no impact. I have used it in back sweetening since it has a higher sweet flavor, but looking at cost per pound, not worth it.
* Glucose will also ferment out 100% therefore no impact.
* Honey is a complex mix of sugars, protein, mineral, acid. It will contribute significant flavor. It is slow to clear as a fermentation feedstock. Honey contains non fermented sugars therefore will have significant residual sweetness and will produce a higher gravity when finished. Seems to ferment slower than table sugar. The flavors build with time therefore at has more impact if aged 2 years. For back sweetening it has good flavor impact, however it will also give turbidity so if you want crystal clear you again would age several years. Have not tried it but some recipes boil honey to denature proteins so it will clear faster. Boiling also seems to increase the non fermented sugar if you put it in the primary.
* Dextrose is readily available. It is clean starch which has been hydrolyzed. There are several grades labeled by d.e. A less hydrolyzed grade will contribute mouth feel/ body but not flavor. Beer folks use it.
* Maple syrup can contribute a maple syrup to a burnt woody note depending on the darkness grade. It mostly ferments out so seems not to change the sweetness.
* there are various syrups available example “rice syrup “ they are usually produced with some protein and mineral content. Flavor is clean and buyers like the hypoallergenic reputation.
* Sorgum syrup, haven’t had to work with it, a guess is it depends on how dark/burnt it is.