  Let A and B be finite dimensional simple real algebras with division gradings
by an abelian group G. In this paper we give necessary and sufficient
conditions for the coincidence of the graded identities of A and B. We also
prove that every finite dimensional simple real algebra with a G-grading
satisfies the same graded identities as a matrix algebra over an algebra D with
a division grading that is either a regular grading or a non-regular Pauli
grading. Moreover we determine when the graded identities of two such algebras
coincide. For graded simple algebras over an algebraically closed field it is
known that two algebras satisfy the same graded identities if and only if they
are isomorphic as graded algebras.
