As long as the diameter of the arbor hole on the stacked dado blade set matches the arbor diameter of your table saw or radial-arm saw—and the arbor is long enough for a dado blade—you can use an 8-inch dado blade on a 10-inch table saw.
8-Inch vs. 10-Inch
There are a couple of reasons why you don't need a 10-inch dado blade set. Since dadoes rarely need to be cut deeper than about 1 1/2 inches, an 8-inch dado blade set will be large enough to cut most dadoes and rabbets.
By making the dado blade set only 8-inches in diameter, there is less weight to the blade set, which lightens the amount of effort that the saw must put forth to cut a wide, deep dado. It stands to reason that the smaller-diameter blade set likely costs a little less than a 10-inch set (since there's less steel needed to build the blades and chippers).
Check the Arbor Size
When buying a stacked dado blade set, be sure that you purchase a set with the correct arbor hole size for your saw. Most modern table saws and radial-arm saws have a 5/8-inch arbor onto which the blade will fit. However, there are a few rare instances where a saw doesn't have a 5/8-inch arbor or the blade set doesn't have a 5/8-inch arbor hole.
A blade with too large of an arbor hole simply can't be balanced properly for use. Conversely, if your blade set has an arbor hole too small for your arbor, resist the temptation to drill out the arbor hole, as you may not only put the blade out of balance, but the heat from drilling may alter the temper of the blade.
Check the Arbor Length
Some table saws have short arbors that can't safely accommodate a dado blade, or they can take a dado blade up to a certain thickness but no more. The rule of thumb here is that the blade must fit on—with the washer (never omit the washer) and nut—so the arbor extends at least a little bit beyond the nut. In other words, the nut must be fully threaded onto the arbor plus a bit more. If the nut is only partially threaded onto the arbor, the nut might come loose during the operation.