Is there any real difference between those two modules? If so what is that?
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]).
A gyro measures rotation rate and in a 3D system that can only be around 3 axes: roll, yaw and pitch. Like Jim says the other 3 parameters may be from an accelerometer, that also gives you a rotational position around those same 3 axes.
You need 6 parameters to describe an objects position and orientation: distance in X, Y and Z direction, and rotation about X, Y and Z axis. The gyro/accelerometer may help you with the rotation, but can't detect lateral movement. (The accelerometer may indirectly measure displacement, but needs a double integral for this, which may compromise accuracy.)
I believe a "3 axis gyro" is exactly what it says, and a "6 axis gyro module" is a 3 axis gyro plus a 3 axis accelerometer.
I'm confirming the question about a 6-axis gyro system. It is used to correct radar images on a sailboat. The primary pitch, roll, yawl are the typical 3-axises and the rotation acceleration for each axis is the second 3-axises. Why? Well on a boat you have a very complex movement, even more so than an airplane. On a boat you're pushed and tipped sideways by the wind and up an down by the waves and sliding off axis by the current. The complete rotational MOMENT is very useful to correct the radar image. Especially when you consider that the radar is mounted on a mast well above the center of mass.
Having said all of that the 6-axis difference over the 3-axis gyro (or if you will fluxgate accelerometer) is a small benefit, so.. often a 3-axis will do the job. However an aircraft carrier in rough seas when trying to land a fighter jet with a side wind and a nervous pilot will always prefer the 6-axis. We can all thank Mr. Isaac Newton for this tid bit.
I think they call it a "6 axis gyro" is because the gyro function and the accelerometer function are done by the same device, the "gyro". This is to differentiate between the simpler 3 axis gyro only devices, as the two are essentially the same part, there is no separate accelerometer, it's just an added functionality to the "gyro" that costs little to nothing to add, but they can add big money to the pricetag of the model for. This is how the "flybar" went extinct, the 3 axis gyro made it obsolete when it replaced the one axis "heading hold" gyro for next to nothing in added cost.