6 degrees of freedom are the 6 different directions something can move in the cartesian plan. You know x,y, z, direction.
x being left and right
y is forward and back
z is up and down.
So the 6 degrees come from what is called translation and rotation in those axis.
Translation is moving back and forth and rotation is turning in that axis.
This is just not answering your question because the answer really is "they are both the same" but I thought I would at least let you know what 6DOF actually means.