Understanding Equivalent Wyckoff positions I'm somewhat confused by the concept of Wyckoff positions in crystal structures. From Quantum Chemistry of Solids by Robert Evarestov, the definition of a Wyckoff position is "all the crystallographic orbits which have the same (not only isomorphic, but the same) site-symmetry group". I was okay with this, but he then went on to define equivalent Wyckoff positions as positions such that "equivalent sites have the same point-group symmetry and the same orientations of symmetry elements with respect to the lattice". 

What I fail to understand is how the equivalent Wyckoff positions don't collapse to a single Wyckoff position, as they seem to meet the criteria of having the same site-symmetry. Is there a clear explanation of what distinguishes two Wyckoff positions enough to be equivalent, but not just a single position?

To clarify my question a little more, here is the specific example given in the text for the space group 136, also called P42/mnm or $D_{4h}^{14}$. 


  Pairs of Wyckoff positions a-b, f-g, and i-j have isomorphic site-symmetry groups 
  ($D_{2h},C_{2v},\text{ and } C_s$ respectively). As is seen from the table, the pairs of points a-b and f-g not only have isomorphic, but also equivalent Wyckoff positions. The equivalent sites have the same point group symmetry and the same orientations of symmetry elements with respect to the lattice.
It seems to me that care has to be taken with the words 'equivalent'  and 'same' in the definitions above. Equivalent positions do not mean the same position. In the case, say, of a 4 fold axis any point say in the first quadrant can be replicated to the other three quadrants and these are equivalent points but not the same point, clearly. In some cases such as with reflections in a plane, two sets of identical (or equivalent) points may be produced and so and the number of equivalent points is reduced. The number of equivalent sets is called the multiplicity. These have been called special positions when they lie on a symmetry element 

In the Wycoff notation equivalent positions are labelled consecutively $a, b, c\cdots$ starting with $a$ for the highest symmetry. A position 2f, for example, indicates two equivalent atoms at position given by symmetry f. For each space group a table of general and special positions can be made.  This includes point symmetries, positions multiplicities and Wycoff symbols. The table below shows examples.


Table copied from  page 75 of 'Introduction to Crystallography' by  D. Sands, publ. Dover