They are not member of the same species although they fall under the same genus which is Ursus.
Brown bears (Ursus arctos) are large bear species widely distributed in the northern Eurasia and North America. Brown bear has 15 known species which includes the very famous grizzly bear (Ursus arctos horribilis). Most of the brown bears are endangered and some of them are extinct (Atlas bear and Mexican grizzly bear).
Polar bears (Ursus maritimus) on the other hand have varying number of species since there are issues in its etymology. Earlier, Polar bears thought to belong on a certain genus which is Thalarctos. However, findings showed that polar bears are included in the Ursus genus. This species of bears are endangered as well.
Polar bears and brown bears are different species of bear. Grizzly bears are a subspecies of brown bear, which makes them a separate species from polar bears. Different species are defined as having reproductive isolating mechanisms that prevent significant genetic exchange in the wild, even where their ranges may overlap. Subspecies are groups of a particular species that share some morphological characteristics and that are located in a particular geographic area. Polar bears evolved from brown bears about 150,000 years ago. They can still produce viable hybrid offspring with brown bears, but they almost always mate within their own species instead. The evolution of polar bears from brown bears is a great example of how speciation often works. A new niche became available (hunting seals on the sea ice) that a certain population of a previously existing species (brown bears) was able to exploit. They started evolving through natural selection to become better adapted to that niche, while other populations of brown bears stayed in their old niche and continued to adapt to it. Eventually the bears in the new seal-hunting niche adapted so much they became a new species, while all the other populations of the original species continued as they always had. What once had been a single species had now split to become two species.