The public mines are shared with everyone at your letter. A plot mine is yours.
What a plot mine is
Claim a plot, and the mine on it belongs to you: you decide what it spawns, who can stand in it and who can break anything. It is a second income next to the A to Z ladder, not a way around it. Mine letters still only move when you mine, and no plot mine has ever paid for a /rankup on its own.
Upgrading it
A new plot mine spawns cheap blocks, the sort Mine A is full of. Upgrade it and it spawns better ones, which means every swing in it is worth more and every plot miner working in it earns more. The upgrades are paid for in prison cash and tokens, like everything else that makes you stronger here.
Plot miners
Plot miners are the reason to build the plot up. Hire them and they work your mine for you, breaking blocks while you are somewhere else on the server: at a KOTH, on a boss, or halfway through Mine T. Each one you add digs through your mine faster, and a well-upgraded mine with miners in it quietly funds the rest of your grind.
They are workers, not a replacement for you. They work the plot they are hired on and nowhere else.
Plots and gangs
You can keep a plot to yourself or open it to your gang, which is what most gangs do: one upgraded plot mine that every member can work is worth more than eight neglected ones. Set who can build, who can mine and who can change the settings.
What it costs
The plot, the upgrades and the miners are all bought with what you earn in game. None of them are in the store: there is no plot package, no miner package and no way to buy a head start on one.