One abbreviation, two different things — the country a garment comes from, and the certificate that attests to it
The abbreviation COO gets confusing in supplier conversations about apparel shipping documents. Imagine a buyer asking for a COO for a shipment going to Costa Rica while an exporter explains one is not needed: they may both be right, because they are talking about two different things. One means Country of Origin — a fact about where the goods were made. The other means a Certificate of Origin — a formal document attesting to that fact.
A Certificate of Origin (often abbreviated C/o, CO or COO) is a document used in international trade: a printed form completed by the exporter or its agent and certified by an issuing body, attesting that the goods in a particular export shipment have been wholly produced, manufactured or processed in a particular country. It is generally an integral part of the export documents. Country of origin, by contrast, is the country of manufacture, production or growth where an article or product comes from — under differing rules of origin in various national laws and international treaties.

Country of origin matters to export documents and to garment labels alike. Products covered by the Textile and Wool Acts must be labeled to show the country of origin: imported products must identify the country where they were processed or manufactured; products made entirely in the U.S. of materials also made in the U.S. must be labeled 'Made in U.S.A.' or an equivalent phrase; products made in the U.S. of imported materials must be labeled to show the processing or manufacturing done in the U.S. as well as the imported component; and products manufactured partly in the U.S. and partly abroad must identify both aspects. The country-of-origin markings guide covers the customs marking side of the same shipment in more depth.
U.S. Customs and Border Protection has country of origin labeling requirements separate from those in the Textile and Wool Acts and Rules. For example, the FTC rules do not require labeling until a textile product is in its finished state for sale to the consumer, so textile products imported in an intermediate stage may be accompanied by an invoice carrying the required information in place of a label. Customs, however, may require an unfinished product to be marked with its country of origin. Manufacturers and importers must comply with both the FTC and the Customs requirements — satisfying one regulator does not satisfy the other. The FTC's textile labeling guidance, linked in the references, works through the labeling requirements in full, and the care labeling guide covers the companion label most garments also carry.
Rules and regulations change, so check with the appropriate agency for the current requirements before a production run is labeled — do not rely on any summary, including this one, for a live shipment. And yes: a COO is also a Chief Operating Officer, which is exactly why spelling the term out on shipping paperwork saves confusion.
It can mean two different things: country of origin — the country where a product was manufactured, produced or grown — or a Certificate of Origin, the certified document attesting to that origin for a specific export shipment. Spell it out to avoid confusion.
No. They are separate requirements. The FTC's Textile and Wool Acts rules govern labeling for the consumer, while Customs has its own marking rules and may require origin marking even on unfinished goods the FTC would not yet require to be labeled.
Products covered by the Textile and Wool Acts must be labeled with their country of origin: the country of processing or manufacture for imports, and specific 'Made in U.S.A.' or combined-origin wording for U.S. products depending on their materials and manufacture.