Jerry is right, there are bigger issues with English. As an Australian, we never really say faucet! It's a tap. Tap is the entire thing, including where the water comes out. For me a nozzle is something that gets attached to something else, but a spout flows freely.

In my opinion, there doesn't appear to be much rhyme or reason to the various collocations that "spout" and "nozzle" pair with. Simply going off my experiences as a native speaker of American English, it would appear that "spout" is used more for household items "faucet spout", "teapot spout", whereas "nozzle" is used for things used outdoors/commercially, such as "gasoline pump nozzle."

The faucet is a spout/nozzle, but refers to the common water outlets such as in bathrooms. So I would never say "faucet spout", but just "faucet".

I suppose the choice is a convention that has been agreed upon through usage over the years. I wouldn't think too much about it. Try and learn from what you see and hear in this case. There are bigger, more important things to learn.

They even use both in one product description: Water Saving Faucet Aerator Kitchen Tap Adjustable Nozzle Spout Hose Swivel) Use google images to find what you need))