Polar bears and woolly mammoths were contemporary, though just for a very brief period. Mammoths came out of Africa nearly 5 million years ago, and then died out probably around 10,000 years ago, though the most recent mammoth remains, from Wrangel Island, date to as recently as 3700 years ago.
Polar bears evolved from grizzlies about 30,000 years ago. Which possibly makes them the youngest species of megafauna on the planet, though I don't know for sure. Wood bison might be younger (but are they a species or a sub-species??), or some other beast. Anyways, the point is, for about 20,000 years polar bears and woolly mammoths frolicked together on the tundra.
Did you know woollies are more closely related to African and Asian elephants than the two types of elephants are to each other? Crazy eh? And there's a population of grizzlies on Alaska's ABC Islands (Admiralty, Baranof and Chichagof) that is more closely related to polar bears than mainland grizzlies. Thus it seems likely that maritimus evolved from this isolated population of horribilis.
I'm not a geneticist so I only have a murky grasp of how they figure those things out.