>>>Pure physics vs practical use here I think.
Yes, but in fact we ARE talking about pressure, for back flushing the filter. Not force.
FORCE is what you are applying to the plunger of the syringe. This is transmitted to the water via the plug at the end of the plunger. A smaller plug means more force per unit area, thus higher PRESSURE.
Ergo, smaller syringes generate higher pressures for a given force applied to the plunger. Likewise, there is a reason that bicycle pumps are long and skinny.
18g needles are used to irrigate because they will give high volumes of flow than e.g. a 27g needle. It has nothing to do with pressure.
Attach the tubing to a pressure transducer on one end and a syringe on the other. Place a standardized weight on the syringe plunger. Try this with both a 10cc and a 60cc syringe. Yes, the 10cc syringe will produce more pressure than the 60cc syringe. I'm not making this up, I swear.
Granted, yes, for practical matters you would want a certain minimal volume of water to back flush with, so there's a sweet spot there somewhere. A 0.5cc tuberculin syringe is not going to be practical for back flushing, no matter how high a pressure it generates.