Dan,

No the resistance is NOT the same. That is why the current handling
capacity is different. Your meter is not sensitive to small fractions
of an ohm, but the relays he is controlling ARE if the wire is long
enough and the voltage is marginal. You could get a reference book on
wire and it would give you the ohms per thousand feet. It is different
for every gauge of wire. Then calculate the fraction of 1000 feet that
yopu are using to get the total ohms. Remember to measure the total
length, not just what you are adding. Then double it because the
current has to flow both ways, out in one wire and back in another.

Stretch