An isomorphism preserves the order of an element. Therefore if, for example, there are strictly more elements of order in than in then theese groups are not isomorphic.
The dihedral group of order 8 can be seen as the group of symmetries of the square. There are two diagonal symetries, which are involutions, therefore (with your notation) contains at least 2 elements of order 2; that is sufficient to prove what you want.
has exactly 5 elements of order 2 (two diagonal symmetries, 2 lateral symmetries and one central symmetry) and 2 elements of order 4 (one rotation of and its inverse).