Full definition
Supplier is defined as: A supplier is any external organisation that provides goods or services to your business under a commercial arrangement.
Supplier is the broadest term in this space. It covers everything from a stationery reseller to a strategic outsourcing partner. The word says nothing about criticality or risk on its own - that comes from segmentation.
In many organisations supplier is used interchangeably with vendor. Where the distinction matters, supplier tends to imply an ongoing service and vendor a one-off product sale.