How the four connect
Concentration ties them together: how much substance sits in each millilitre of liquid. Divide the amount in the vial by the volume of liquid added and you have it. Divide the amount you want by that concentration and you have a volume. Multiply that volume by one hundred and you have the mark on a U-100 syringe.
Adding more liquid never changes how much compound you have. It spreads the same amount through more volume, so the same quantity occupies more marks on the syringe. That is the entire relationship, and it is the only thing the calculators on this site do.