What is da difference between a complementary product and a supplementary product?

In products, they mean the same thing - two products working together. An example of this is a brand of mobile phone sleeves that matches a brand of mobile phones.

A supplementary product is one that allows another to function, like refills for a ballpen. More commonly though, a supplementary product is a term used in economics for a good that does not substitute another good but for which the demand rises when the price of another good increases.

When the price for gym membership rises, the demand for hometrainers increases, as an example.