Keeping your nose to the grindstone means continuing to work; paying attention. It actually comes from old grist mills, which had big turning stones for grinding grain into flour. The stones, which were several feet across and weighed tons, had to be adjusted precisely so they ground the grain, but didn’t grind against each other. If they did, that would wear them out, not to mention getting sand in your flour. The way the miller kept the stones adjusted was not by eye, but by smell. If the stones were too close together, the grain would begin to burn, and the miller could smell it and make a quick adjustment. But to be quick enough, he had to “keep his nose to the grindstone” — in other words, stay close enough to catch the first whiff of burning grain.
Grist mills were important institutions in their communities, and nearly everybody in a village visited because it was the only place to get flour or other ground grain. So they all knew how big and heavy the mill stones were. When somebody referred to a big problem as “having a millstone around your neck,” it was obvious what they meant. That phrase entered the language too.
Once you have huge grindstones turning by either water, wind, or animal power, you can grind nearly anything. Whatever you put in the hopper is “grist for the mill.” “Grist” actually means “an amount of grain (originally corn) to be ground.” Nowadays “grist for the mill” means “anything can be used.”
Getting ground into flour is, you’d expect, pretty hard on the grain. That’s why the phrase “going through the mill” or “been through the mill” means undergoing great hardship. It’s not, or at least you hope it’s not, a “run of the mill” experience. “Run of the mill” being ordinary or everyday. It probably refers to the mill operating all the time, or at least whenever somebody stopped by with some corn or wheat to be ground up.
it’s also possible that “run of the mill” didn’t come from grist mills at all, but from a later kind of mill: either a textile mill or a lumber mill. Those kinds of mills were bigger and more industrial — factories, really, that produced all sorts of cloth, or wood. So “run of the mill” could have originated from them, meaning whatever the mill produced at a given time. “Run of the mill” also seems to be more recent than the other “mill” expressions; it only dates from the late 1800s. The others are hundreds of years older.
Nevertheless, that’s about the end of the English expressions based on mills, grist or otherwise. There’s nothing more to see here; move along, stop milling around and go visit a reenactment like the Plimouth Grist Mill in Plimouth Plantation in Massachusetts in the US. It’s a working restoration of a water powered mill, and they’ll demonstrate “keeping your nose to the grindstone” — you can even try it yourself.