In normal use the dead center would be used in the spindle as it turns with the work, such as when using a lathe dog. The live center is usually used in the tail stock. You can use a dead center in the tail stock, just be sure to lube the center hole in the part and check the tension from time to time as the part will change length as it heats up from turning it. If wanting a live center, you can spend little or a lot. You are buying precision, less run out, with the pricier centers.
This is the same way that one would not go gather a "f a g g i t" of sticks anymore.