What is the difference between symmetry and hermitian ?

Question

I am really confused now.

Transformation, T , is called hermitian if ( T(x), y ) = ( y , T(x) )

Transformation, T , is called symmetric if ( T(x),y)=(y, T(x))

I think that difference between these two is whether it is real or complex euclidean space.

In euclidean space, inner product is complex number.

If T is hermitian, then how can (T(x).x)=(x.T(x)) be true with no conjugate sign?