They form tubers,which will grow slips that you cut off and root.Most are grown from cuttings that will root and overwinter in the house.Seeds,I have never heard of,but if you grow from the tuber they are referred to as seed potatoes.

I have never seen any seeds on the new chartreuse or purple varieties either, but here in Hawaii if you wish to take cutting from the plant, put them in water you will have new roots growing within 2 days, Pot up and you have a new plant. By the way I understand that the tubers are edible just like normal sweet potatoes.
Jenny

I got seeds from my sweet potato vine last year and started them idoors, I got quite a few new vines with purple flower but didn't get any new seeds from these plants.