(1) Originally, an OEM (original equipment manufacturer) was a company that supplied equipment to other companies to resell or incorporate into another product using the reseller's brand name. For example, a maker of refrigerators like Frigidaire might sell its refrigerators to a retailer like Sears to resell under a brand name owned by Sears. A number of companies, both equipment suppliers and equipment resellers, still use this meaning.
(2) More recently, OEM is used to refer to the company that acquires a product or component and reuses or incorporates it into a new product with its own brand name.
ODM stands for Original Design Manufacturer.
An ODM company is a company that both designs and makes products or components. These products or components are sold to another company which sells them under the company’s own brand name.
An ODM can also be a company that re-uses or incorporates a specific solution or product into a new product, under its own brand.
Party A chooses party B's products and asks party B to produce with Party A's brand logo. That is called OEM
Party A owns technology and designs, and asks Party B to produce according to Party A's requirements. That's called ODM.