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The short answer is that a size 14 darning needle is probably larger than a size 18. I say “probably” because I don’t know where you live and what needle gauge scale has been used to label the needles you are considering.
The standardized scale for defining wire diameter in the United States and many other countries is called AWG for American Wire Gauge, or Brown and Sharpe Wire Gauge, after the guys who came up with the algorithm.
AWG is used for most types of wire and needles; though not for steel. The steel industry uses different numbering systems for their wire thickness gauges. There is a U.S. Steel Wire Gauge, the Music Wire Gauge and the W and M Wire Gauge, to name a few.
I’ve probably got you even more confused at this point, right? But here’s the bottom line: every wire gauge system I am aware of uses an inverse scaling system. That means as the gauge numbers go up, the diameter of the wire goes down. So a size 18 needle would be thinner than a size 14.
Most likely the needles you are looking to buy are labeled using AWG. This chart shows how the diameter decreases as the gauge numbers increase.

This man shall be darned forever!
P.S. Some manufacturers of knitting and crochet needles have opted out of the inverse wire gauge scales and so their needles sizes thicken as the numbers go up. These are simply numbers like clothing sizes; not mathematically precise gauges.
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