Klein 4 group ismorphic to D4?

Klein 4-group is a symmetry group of rectangle (or rombus). And as far as I understand it is not isomorphic to Dihedral group of order 4. Because Dihedral group of order 4 is a group of rotations of square.

If this is true then why Wiki says that they are isomorphic:

The Klein four-group is the smallest non-cyclic group. It is however an >abelian group, and isomorphic to the dihedral group of order (cardinality) 4

What am I missing here?

The dihedral group that is the symmetry group of a square is of order 8 and usually is denoted $D_4$.