Yes, the stops are the same measurement, but you are misunderstanding what is meant by dynamic range. Dynamic range is not the same as an exposure setting.

Dynamic range is everything from black to white (i.e., the points at which you lose detail into black and white) that your camera can capture. So, if you have to think of it in exposure terms, if you take a picture that encompasses black and white, and if you were to expose the black so it appeared as middle gray, and then exposed the white so it appeared as middle gray, the difference in your exposures would be whatever the sensor's dynamic range is. That's why the difference is so large. Think in terms of the ends of your histogram, not the middle.

In terms of how -3, 0, +3 is only 6EV, well, it's a 6EV variance, but of the entire dynamic range. So, if say, you have a sensor with 12EV DR, you've taken that 12EV and shifted it a total of 6EV, so you've got 18EV of dynamic range possible in your HDR image. But it really depends on the scene you're shooting as to whether or not you actually used all of that range. Simply shifting exposure by a set amount in both directions is no guarantee you've covered the entire dynamic range of the scene. Or that your scene requires any bracketing at all to cover its dynamic range. Not all scenes have a dynamic range outside the capabilities of the sensor.

This is why some HDR folks will use the histogram to make sure they need to bracket, as well as to see that they've covered the data to extinction at both ends. And why the MagicLantern HDR nuts have found a way to automate this. :)

See also: Cambridge in Colour's "Understanding Dynamic Range" article.