When I read about how to select wire gauge, it talks about length of run and amps.  This part I understand.  However, I'm installing some LED light strips.  These lights will be powered by a 24V output power supply.  

These LED bars say you can connect 10 or 16 feet of them in a chain, depending on how many connections.  The real limit is 10 connections.  There are 1 ft and 2 ft bars, hence 10 and 16 being different.  Basically, they are calling out that the real limit is 10 connections. 

Since the real limit is the number of connections, I think I can inject a 20 foot length of wire between bars.  In trying to calculate the wire gauge for this segment, I use 5 Amps and 20 feet, which gives me a conservatively sized 14 AWG wire.

AND MY QUESTION:

I understand the math behind the 14 AWG wire as cited above.  However, once the run of LED bars starts, each segment is then connected with a 22 gauge wire.  And, if I didn't need the extra length, the wire they ship with, for connecting the power supply to the head of the light bars, is also 22 gauge.  

Why does the math call for a larger gauge wire, while the appliance connecting to it has much smaller wires?  Aren't those smaller wires to the device carrying the same current?  Why can they be smaller?