COC
A Certificate of Origin (CoC) is a document that indicates the origin of the product. A CoC therefore proves in which country a product is made.
Some countries outside the EU ask for a CoC because of trade policy measures, such as boycotts, import restrictions and import quotas. In some countries with a CoC you also have to pay less or even no import duties at all. The MFN import rate (most favored nation rate) then applies there. Without a CoC you can run into difficulties if you want to import products in a certain country. You usually do not need a CoC within the EU.
Based on a CoC, a country can decide whether or not you can import a product. And the country also examines with a CoC whether the MFN import rate applies.
EUR1
You need an origin document for export to many countries outside the EU. This document explains from which country a product comes. A Certificate of Origin (CoC) is usually used. Do you export to countries with which the EU has concluded a trade agreement? Then you use a EUR.1 document or a EUR-MED document. These documents entitle you to a reduction or even exemption from import duties.
EX-A
When goods need to be exported outside the European Union, you need an EX-A document. An EX-A document is an export document which is required when a shipment, that has been originated in the EU (or has been Customs cleared in the EU), leaves the European territory. So it is about goods which will not be returned to their origin.