Hobbies And Interests
Specific vs. General
Tundra refers to one specific area -- the area south of the Arctic Ocean where it is too cold for trees to grow. Polar regions, on the other hand, are any area near the north or south pole. This is their only prerequisite. A polar region can be on land, in the ocean or somewhere in between. A polar region doesn't even have to be on Earth; Mars, Mercury and every other planet also have poles, which means they also have polar regions.
Temperature
The tundra is characterized by extremely cold weather, never exceeding 20 degrees Fahrenheit in the winter. Polar regions have extremely cold weather (as they are farther away from the equator than the tundra), but this is not what characterizes them. They are cold because they are polar, not the other way around.
Area
Tundra is the area between the 75th and 60th parallel latitudes. Polar regions, on the other hand, are the areas around the poles. They aren't specific, and there are two polar regions on the planet, while there is only one tundra.
Seasonal Differences
Seasonal differences are more pronounced in the tundra than they are in the polar regions. While both areas are extremely cold, the snow does melt in the summer (although the frost in the soil does not). Due to the permafrost beneath the tundra, the snow has nowhere to go, and it collects in pools and marshes. Polar regions, by definition, are closer to the poles, so they have much less snowmelt than the tundra does.