Between the two varieties I cannot say as I only have DK.

Now as for a good cold Hardy fig that taste good and produced good after winter die back. MvsB, Sal's G, and connies dark. Connies being the larger.

I am testing a few more for cold hardiness this winter. Violetta bayerfeinge, and nordland. We will see how it goes.

No. They are not the same.

What zone are you in. Here in my zone 6/7, your benchmarks would suit what I have in-ground like Desert King, Conadria,
Osborne Prolific, Verns BT, Latarrula, Granthams Royal, Longue d'Aout

Longue d'Aout was the largest fig in my yard.  One of the sweetest with very good quality flavor.  It had winter die-back but grew from the roots and still gave me 14 figs this year.  My tree is 2 years old.

Shipping to a foreign country is difficult, it depends on Korea's import laws.  Here in the US if we get a foreign shipment of plants without permits the govt comes and takes it, and sometimes takes all your plants.  So here it is not worth the risk, plus the potential for importing invasive insects or plant diseases.