My brother brings me a load of citrus wood every spring. I've used orange, lime, lemon, grapefruit, and tangerine. Never used store bought citrus wood, but I think it would be the same.
Citrus is great on chicken, fowl, and seafood. (I have used it on pork as well.) The citrus smoke has medium (not heavy) smoke flavor and it gives the meat a nice golden color. If you use it on mild flavored meats like chicken, it has a slightly sweet but tangy property much like the smell of the orange blossom itself. However if you use too much wood it will make the meat overpowered with smoke and slightly bitter.