In context of trade receivables, the term assign means to pledge trade receivables to a lender (person/ entity providing loan) as collateral for a loan.
In context of cost accounting, this term means to apportion, apply, spread or allocate production overhead costs to the product.
An assignee is an entity who receives the transfer of title, property or rights from a contract. The assignee receives the transfer from the assignor. For example, an assignor may transfer the title to a piece of property to an assignee.
An assignor is an entity who transfers the rights associated with a property to another entity. For example, an entity (the assignor) that enters into an agreement to sell a property can assign the profit it will receive from the above mentioned agreement to another third party (the assignee) such as a charity foundation or a trust.