We explore the basic physical origins of the noncrystalline and crystalline components of the anisotropic magnetoresistance (AMR) in (Ga,Mn)As. The sign of the noncrystalline AMR is found to be determined by the form of spin-orbit coupling in the host band and by the relative strengths of the nonmagnetic and magnetic contributions to the Mn impurity potential. We develop experimental methods yielding directly the noncrystalline and crystalline AMR components which are then analyzed independently. We report the observation of an AMR dominated by a large uniaxial crystalline component and show that AMR can be modified by local strain relaxation. Generic implications of our findings for other dilute moment systems are discussed.