With the habitats of both Polar Bears and Grizzly Bears converging, how is it possible that these two distinct species are able to produce offspring called 'Pizzlies'? Does this mean these two species are actually one?
Tl;dr: 1. Easily. 2. No.
First, "species" is a term that has maybe 40 different definitions, if not more. It's a human-made distinction, not a natural one, between different populations of living things.
It sounds as if you're thinking of the ever-popular definition of "two kinds of creatures that cannot interbreed and produce fertile young." This is the one that's most often taught in grade school in the US, probably because it's easy to explain to small children. Then the mule is trotted out to show that horses and asses are two different species. But this is not the best definition or even much used by scientists, for a lot of reasons I won't go into here.
As a definition, it really doesn't work with grizzly bears and polar bears. The ancestors of polar bears split off from brown bears, and rather recently, too (probably half a million years ago or less), and the two populations have been mating with each other intermittently ever since, which has done a lot to confuse genetic studies. The two species have only stayed separate because polar bears make their living in a very different niche and in a very different way from brown/grizzly bears. So they don't meet with each other very often - or at least they didn't until the recent extreme warming of the Arctic, which has damaged some areas of polar bear habitat to the point where the bears have been forced to go inland in a desperate search for food.
So, if you define "species" by the pop-science definition, they are the same species - they can certainly breed freely together. By most other definitions, they are separate species. Their very different lifestyles and their very different adaptations have kept them recognizably separate right up to today.