ISI mark is given by BIS. this is a third party gurantee of quality. BIS does certain checks on the product and provides and gives this ISI Certificate

Whereas ISO is a system ...international organization for standardisation ... companies work for this system for standardisation of process ... this gives an image of the company to their customers ans also improves the quality culture of the company

ISO (International Organization for Standardization) is the world's largest developer and publisher of International Standards. ISO is a network of the national standards institutes of 158 countries, one member per country, with a Central Secretariat in Geneva, Switzerland, that coordinates the system.

Whereas ISI is Indian Standards Institute which is renamed as Bureau of Indian Standards.

ISO is a quality management system standard which standardizes and documents the various activities of the organization like purchase, stores, sales, processing, it focuses on customer needs and fulfilling the same hence enhancing the satisfaction levels and laying and implementing the systems for continual improvement. However ISI mark means the product conforms to respective national product standard the customer has to accept the same.