Just to substantiate that I am a "knowitall" (if that is the right word) NEMA means National Electrics Manufacturers Association. It is not a company, so no product piracy possible there.
The NEMA 23, 32 etc. solely refer to flange dimensions and bolt mounting patterns. Nothing to do with manufacturer, torque, voltage etc.
The only take is that usually bigger flange motors have bigger shafts, draw more current and have more torque.
There are exeptions, so a long high torque NEMA23 motor can have more torque than a "pancake" NEMA32.
As for a DIY router built. More bigger motor more better.....
p.s. after looking at the pictures. They look like NEMA17. "Possibly pathetic", just get bigger ones that can move some machinery.

For routing or milling you will not get anywhere with this. If you want to engrave some nameplates or want to drill some tiny holes, you might get away with it.
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pps.: does not matter so much, you can figure out where the coils are at (my guess is 1st pin & 3rd pin for coil 1.... 4th pin & 6th pin for coil 2),
You will find lots of instructions how to figure out the pins on youtube. (tip someone gave me: just connect pin 1 & 3 and try to spin the motor by hand, if that is difficult you found a coil)
Connect them to your motor driver. Set driver to one amp amp current, if they overheat reduce current. If they are cool enough to touch after running a while you can increase current. If they burn down, buy new ones.
That is what I always did with 2nd hand steppers and so far no fire, no damaged motor.