In supply chain and EDI language, the company at the center of the relationship is usually a manufacturer or brand, a retailer or a distributor. Everyone it trades with is a trading partner: the suppliers it buys from, the customers and dealers it sells to, and the carriers and 3PLs that move and store its goods.
The role depends on the relationship, not the company. A distributor is a customer when it buys from a manufacturer and a supplier when it sells to a retailer. A manufacturer is a supplier to its own customers and a buyer from its component suppliers. That is why trading partner programs are usually organized by process: procure-to-pay on the buying side and order-to-cash on the selling side, with logistics running through both.
An EDI trading partner is one that exchanges standard electronic documents with you. Many trading partners connect only part of the way, or not at all: a non-EDI trading partner may send PDFs and spreadsheets, while a hybrid trading partner uses EDI for some documents and other channels for the rest. Each one still has to follow your rules if your data is going to stay clean.