The latter, original equipment manufacturer is the better known term and refers to a third party manufacturer who manufactures either sub assemblies or entire items to be sold by a vendor, usually under the vendor’s brand. OEM equipment is usually made to a specification or design supplied by the vendor.
By contrast, an ODM or original design manufacturer, refers to a manufacturer who develops a design on its own account, which it owns, and then supplies to a vendor who sells it under the vendor’s brand name. The underlying agreements in such an arrangement are usually referred to as Originate-Design-Manufacture arrangements.
These acronyms are often misused and mis-described, so care should be taken to understand the actual nature of the relationship between the parties and the services offered.