Toning Muscle
When muscles look and feel tight in a normal, uncontracted state. They appear "defined" when there is little excess body fat. You want to reach for an overall decrease in body fat and resistance training to reach you "toning" goal.
Building Muscle
This challenges muscles and adds more muscle mass through strength training and eating more. Basically it comes down to pick up something heavy that is hard for your body and the muscles react by ripping and getting small tears. When it heals instead of scar tissues, it heals with new muscle fibers. In essence it requires strength gains but from newly grown muscle fibers. Your routine should target the specific muscles you want to increase.