To effect a Branch Transfer of goods, the Registered Taxpayer must issue an Intra-State Delivery Challan (CGST+SGST) and create an E-Way Bill against that Delivery Challan.
The movement of goods across states is a taxable supply and must be accompanied with an Inter-State Tax Invoice (IGST). To effect a Branch Transfer of goods, the Registered Taxpayer in Bihar in must issue an IGST Invoice to the Registered Taxpayer in West Bengal and create an E-Way Bill against that Invoice.
Two E-Way Bills must be generated in this situation. First, the Bihar Supplier will issue an Inter-State Tax Invoice (IGST) to the Tamil Nadu Recipient with Place of Supply Tamil Nadu with a Ship To address of the final Consignee in West Bengal. For this Invoice, an E-Way bill must be generated with Consignor as the Bihar person and Consignee as the Tamil Nadu person.
Second, the Tamil Nadu person (Bill-To Party) will issue either a Tax Invoice or a Delivery Challan to the West Bengal person (Ship-To Party). The Place of Supply of this transaction is West Bengal. For this transaction, an E-Way bill must be generated with Consignor as the Tamil Nadu person and Consignee as the West Bengal person.
Note that the actual movement of goods is from Bihar to West Bengal.
Two E-Way Bills must be generated in this situation. First, the Bihar Supplier will issue an Inter-State Tax Invoice (IGST) to the Tamil Nadu Recipient with Place of Supply Tamil Nadu with a Ship To address of the final Consignee in West Bengal. For this Invoice, an E-Way bill must be generated with Consignor as the Bihar person and Consignee as the Tamil Nadu person.
Second, the Tamil Nadu person (Bill-To Party) will issue a Zero-rated Export Tax Invoice to the person outside India. For this invoice, an E-Way bill must be generated with Consignor as the Tamil Nadu person and Consignee as Unregistered Person (UNR). The destination of this E-Way Bill will be West Bengal sea port.
Note that the actual movement of goods is from Bihar to sea port in West Bengal.
Supply to SEZ is considered Inter-State Supply under Section 7 of the IGST Act. However, the movement of goods is Intra-State. E-Way Bill does not concern the nature of supply, but only the type of movement.
E-Way Bill is needed in states that require E-Way Bill for Intra-State movement. The list of 13 States as of Feb 1, 2018 is available here.