  We deal with the following question: What is the proper way to introduce
symmetric difference in orthomodular lattices? Imposing two natural conditions
on this operation, six possibilities remain: the two (commutative) normal forms
of the symmetric difference in Boolean algebras and four non-commutative terms.
It turns out that in many respects the non-commutative forms, though more
complex with espect to the lattice operations, in their properties are much
nearer to the symmetric difference in Boolean algebras than the commutative
terms. As application we demonstrate the usefullness of non-commutative
symmetric differences in the context of congruence relations.
