Difference between the use of "supplier", "vendor", "provider"

Which is the difference between the use of supplier, vendor, provider? The way I see it, they are complete synonyms. Am I right?

A supplier might not be paid for what he has supplied. A vendor, one who sales, must certainly expect to be paid. And a provider, much like a supplier, might not be paid perhaps, like many health care providers, receive payment from a source other than the person whom he provides a service. All that said, in the appropriate context all three of the words could be synonyms. I am not sure there are many "complete synonyms." If words are completely synonymous wouldn't all but one devolve out of the language? But maybe that's just an understanding I got from Mr. Darwin.

It is often a matter of context, for example,

providing for your family,
wholesale supplying goods for the store
software vendor selling services to

supplying food for your family sounds ankward.