Contractor vs Vendor

My company is ordering a product and/or service from another company. When stating obligations on paper, would the company doing the work, from our point of view, be better described as Vendor or as a Contractor?

What would be the fine differences between the two?

A contractor is a kind of vendor.

Vendor is a relatively general term, referring to a company that sells any kind of product or service. ODO:

A person or company offering something for sale, especially a trader in the street

Contractor refers to a vendor that enters into a contract with the customer. ODO:

A person or firm that undertakes a contract to provide materials or labour to perform a service or do a job

So if the business involves independent transactions, the seller is just a vendor; if there's an ongoing relationship described in a contract, they're a contractor.

However, in many business-to-business situations they're used interchangeably, I think because it's understood that certain types of services are usually provided under contract, so the vendor is assumed to be a contractor.

A vendor does not have to have a written contract. Vendor may provide a service or product requested by the customer and they submit a request for payment. A contractor bids on a service or item and the consumer selects the best bid.