Tyre balancing: whenever you fit new tyres, the wheels must go through a balance procedure, this is required to counter act uneven masses within the tyre and rim assembly so that the wheel will run smoothly when driving. A technician will use a balance machine to detect the imbalance then apply weights to the wheel correct.
A wheel alignment, on the other hand, corrects the various angles of contact that a tyre has with the road surface, which is a completely different procedure requiring specialist equipment.