Summary: In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave (CDW) order. Whether rotational symmetry breaking (nematicity) occurs intrinsically and generically or as a consequence of other orders is under debate. Here we employ resonant x-ray scattering in stripe-ordered \((La,M)_2CuO_4\) to probe the relationship between electronic nematicity of the \(Cu\) 3d orbitals, structure of the \((La,M)_2O_2\) layers, and CDW order. We find distinct temperature dependences for the structure of the \((La,M)_2O_2\) layers and the electronic nematicity of the \(CuO_2\) planes, with only the latter being enhanced by the onset of CDW order. These results identify electronic nematicity as an order parameter that is distinct from a purely structural order parameter in underdoped striped cuprates.