There is such thing as a cross breed between a grizzly and polar bear! It's called a Grolar Bear.
The name is obviously a portmanteau of "grizzly bear" and "polar bear," and it isn’t exactly creative. The fact that these animals exist is pretty cool. Still, it's not exactly something you’d want to run into in the wild.
There have been several cases in recent years where Grolar Bears (occasionally called Pizzly Bears instead) have been seen in the wild. The Grolar Bear is a relatively recent find, only proven to exist in the wild in 2006, when one was shot by an Idahoan hunter in Northern Canada.
The finding lent evidence to the claim that polar bears and grizzly bears have, however, been breeding from time to time for hundreds of years. The hunter had thought it to be a polar bear until closer inspection revealed it had more grizzly-like traits.
Grolar Bears are generally an even split in appearance between their parent species. Their bodies are smaller than polar bears, but larger than grizzlies. They have long necks like polars, but have shoulders more like grizzlies.
The soles of their feet are also hairy like polar bears. They behave like polar bears in their mannerisms. They stamp in the same way polar bears break ice, and hurl objects to the side in the same way polar bears hurl prey.
They also lay down like polar bears: on their stomachs with their back legs spread. This, however, might be mostly because of physical build.