We reveal a striking correspondence between electron- and phonon-driven pairing in twisted bilayer graphene (TBG) by mapping an atomistic electronically driven pairing model onto an effective inter-valley, intra-Chern description, originally proposed for phonon-mediated superconductivity. Within the unified framework of intra-Chern pairing, we then analyze the competition between nematic and chiral d-wave superconducting states. The latter corresponds to the extreme Chern-polarized limit and hosts unpaired flat bands within the superconducting gap, which generally disfavors it relative to the nematic states. Crucially, nematic order is locally preferred at each momentum, but the optimal nematic directions are incompatible across the Brillouin zone due to the broken rotation symmetry. This momentum-space frustration still enables a chiral ground state at large fillings or weak interactions in a symmetric parent state. Including heterostrain or inter-valley coherence further stabilizes the nematic ground state and sets the nematic direction. Under heterostrain, this direction shows a double winding with the strain axis, revealing the d-wave nature of the pairing, while inter-valley coherence makes it filling dependent. Our results thereby provide a unified understanding of superconductivity in TBG, in which electron- and phonon-mediated pairing cooperate, and clarify the microscopic origin of the competition between the chiral and nematic superconducting states.