1. A product search method in a product search system, the method comprising: maintaining a database including a product identifier and a product category of the product identifier; receiving an original query for search of a product from a user terminal, and extracting a category query associated with the original query; selecting at least one product category included in the database using the category query; identifying a product identifier type associated with the selected category; searching the database by applying a search logic corresponding to the identified product identifier type from a plurality of search logics; and outputting a result of the search as a product identifier type that matches the original query.