What is the difference between 3 axis and 6 axis gyros?
There is no "6 axis gyroscope"...

If you read "gyro: 6 axis" somewhere, this is possibly because of a limited knowlege of the person filling in the fields or a limit of the fields given (e.g. there is a description field for "gyro" but none for "accelerometer").

It will actually mean 3D gyro (3 axis) + 3D accelerometer (in 99% of the cases, could be a 3D-compass too).

There are only 3 possible axes for a gyro. So having 6 measurement values, would mean: measuring (at least indirectly) all the axis twice.
This could make sense, if you want to avoid failure of the whole device if one gyro is defective. Also: achieving more accurate measurements. But note that most measurement noise is due to spikes/noise of the power supply. So you would have to have 2 independent power supplies to have really independet measurements (therefore achieving a 3dB improvement of the measurement noise  [=half the noise]).