Is a mechanical injector the same as a mechanical pump?
No. A mechanical injector requires a very high pressure pulse of fuel, the extreme high pressure overcomes the spring in the injector allowing it to open a tiny fraction. That tiny opening causes the fuel to spray out in a highly atomized (little tiny tiny droplets) mist, which is the best way to mix it thoroughly with the air in the cylinder that then allows the explosion (actually a controlled, but very very fast, burn), which is how the magic happens.
A mechanical injector pump is just the means of producing those extreme pressure pulses. They rely on the fact that liquids are, to all intents and purposes, incompressible (not incomprehensible...) a bit like a hydraulic system - only many thousands of PSI. The Lister's mechanical fuel pump is an extremely simple cam-driven affair; a cam on the camshaft pushes a tappet up which squishes the liquid in the fuel line. Since the fuel can't compress, it's forced out of the injector (see above).
Is the mechanical injector superior to a pump + injector?
The mechanical injector requires a mechanical pump to work. The injector on its own does nothing...
More recently, you may have heard of "common rail" diesel engines - very popular in cars. These have a single pressurised fuel line going to all of the injectors; it's at a lower pressure than a mechanical injector pump will deliver, but still many hundreds of PSI. The injectors are then controlled electronically. This has the advantage of only requiring a relatively simple pressure pump (which can be electrically driven), one fuel line, and the injection timing can be changed "on the fly" by the engine's ECU. As Lister CS engines pre-date computerisation by some years, they use the old-style mechanical injection system. Timing it can be a bit of a chore...
I guess what I am trying to get at is why these machines last so long vs something like a Fordson Major SIMMs inline pump or something with a rotary pump, like John Deere/Furgenson 35/Case 188D with the stynadyne/roosa master rotary design
Simplicity, primarily. There's only one cylinder to power, so there's no internal drivetrain, and virtually no moving parts. Plus, coming from a time when longevity and reliability were design goals rather than dirty words (and "built in obsolescence" hadn't been invented yet), they were literally massively over-engineered for the job at hand. Also, most Lister CS engines aren't out in all weathers being bounced around in fields etc... they have a cushy life in their sheds, only subject to their own vibrations.
Obviously the less parts, the less things can break down
Yep, that too.
What I don't want is some weird one off injector that I have to send to a lab halfway around the world to get some .00035 part made, and wait 3 months for it to come back
Injectors suitable for Lister CS engines (original & clones alike) are widely available and not that expensive. Eventually, years & years from now, they'll no longer be manufactured brand new, and years & years after that (when new-old-stocks are depleted), any decent machine shop will be able to repair/re-manufacture one-offs; either that or you'll just duplicate one in your Star Trek replicator...
A diagram or drawing would really help me
What do you need a diagram of? The entire fuel system? A whole Lister CS including fuel system? An injector?
Anyway, I hope the above helps. If anyone spots any errors or omissions, let me know and I'll fix 'em.