By definition,
An incision is (according to Miriam-Webster’s dictionary): “a wound made especially in surgery by incising the body”
A cut is (also according to Miriam-Webster’s dictionary): “to penetrate with or as if with an edged instrument”
An incision *is* surgical, while a cut *can* be surgical but also *can* be not surgical.
So the difference between an incision and a cut would be that an incision is more professional and a cut is less professional.
