You have misinterpreted what the table you referenced means.
First, attached below are the specs on common #22AWG stranded hook-up wire from Belden. It is PVC insulated, 7 strands of #30 tinned copper wire. You want the wire tinned if you plan on soldering it as bare copper wire corrodes rapidly and is therefore harder to solder. This is the standard #22 stranded hook-up wire you would probably get no matter where you buy it or who made it. The #30 individual tinned strands have an area of .049 mil square and 7 strands of #30 would have about .343 mil square. Your table shows that #22 wire has .330 mil square so this makes sense. If the wire was made for test leads like those for a DMM then it probably would have many more strands and silicone insulation to make it more flexible. Some of the higher current test leads I have contain 254 strands of very fine wire.
When you mention the current carrying capacity of the various 'cores' that means that if you make a cable with an outer jacket that has a certain number of wires, or cores, in order to keep the heat radiated by wires in the cable down, you have to derate the current handling capacity of the wires in the cable. It has nothing to do with whether the individual insulated wires are stranded or solid. If you were making a cable, or bundle, of 42 or more wires, the individual #22 insulated wires would be derated from 5 amps to 1.5 amp current capacity as your list shows.