It is indeed frustrating to find distinct words with dictionary entries that overlap to such a degree.
To get at the differences you will need to dig a little deeper, and maybe research the etymology. For example one attempt to differentiate plant and factory
I can think of two distinct situations
- You see an industrial complex, a sign outside says "Car Assembly Plant" or "Biscuit Factory" or "Woollen Mill". Is there a way to deduce which of plant, factory or mill was selected before you see the sign?
- In conversation you want to refer to such a complex, and do not know its allocated name. Will your meaning be clear if you choose the "wrong" word? Is there a best default to use?
Going back to some origins:
Mill has a quite specific root in the grinding, such as wheat into flour, hence windwills. The term broadened to other forceful industrial processes. When I was a boy in Yorkshire my town had buildings where wool was processed into cloth, we called those Woollen Mills, and Lancashire had its Cotton Mills. Hence the stereotypical:
Trouble dahn t'mill
I would say that "mill" implies processing some basic ingredient into something that itself is used by another industrial process. The original meaning comes from grinding, mill-stones grind grain to flour.
- Flour Mill produced flour then used by bakers to make bread and cakes.
- Paper Mill processes wood to paper which is then passed to printers
- Steel Mill processes ore and metals to pre-formed steel sheets and rods for use in other industrial processes.
- Woollen Mill processes wool to cloth used by tailors and milliners.
A factory has connotations of manufacturing, creating complex objects.
A plant is not a word I remember being used in this way (as opposed to a living, growing, organsim) as a boy in the UK, but is certainly common now. I view plant as something larger than a single factory, a huge car manufacturing plant for example. I think plant can describe places where things are processed rather than manufactured, for example a water purification plant.
So to name something a mill we have relatively clear concept. A plant seems a broader term than factory. For things such as a water-processing plant, it's clear that plant is a better term. But why are the Nissan Assembly Plants plants rather than factories? I can think of no reason other than scale.
My default would be to use the word factory. I'd be confident of being understood.