I have a outside water faucet that has threads that are narrower than a standard hose fitting. I have been to a couple of hardware stores looking for an adaptor of some sort with no luck. I show them a picture of the faucet- but they don't know how to help me. Is there a name for the part I am looking for?

Hi Hubba

How about showing us the picture?

It was probably designed for a vacuum breaker that is a smaller thread with a standard hose thread on the out end. May have to replace the hose bib if you cannot find a fitting. Check in the Watts section at HD, they have a lot of adapters.