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The QED interaction vertex couples an electron, a positron, and a photon with vertex factor -ie gammamu. All electromagnetic processes -- Compton scattering, pair annihilation, Bhabha scattering, Moller scattering -- are built from combinations of this single vertex. The coupling strength is alpha = e2/(4pi) approximately 1/137.
Quantum electrodynamics is built from a single interaction: the coupling of an electron (or any charged fermion) to a photon. In the Lagrangian, this coupling appears as L_int = -e psi-bar gammamu psi A_mu, and in Feynman diagrams it is represented by a vertex where an electron line, a positron line (or equivalently, an electron line with reversed arrow), and a photon line meet. The vertex factor is -ie gammamu, and the coupling constant is e, related to the fine structure constant by alpha = e2/(4pi) approximately 1/137.
Every electromagnetic process in nature is built from this one vertex. Electron-muon scattering uses two vertices connected by a single photon propagator (t-channel exchange). Compton scattering (photon + electron -> photon + electron) has two diagrams at tree level (s-channel and u-channel). Pair annihilation (e+e- -> gamma gamma) is related to Compton scattering by crossing symmetry. Bhabha scattering (e+e- -> e+e-) has both t-channel (photon exchange) and s-channel (annihilation) diagrams. Moller scattering (e-e- -> e-e-) has t-channel and u-channel diagrams with a relative minus sign from Fermi statistics.
The computation of any tree-level QED process follows a mechanical procedure. Write down all topologically distinct Feynman diagrams. For each diagram: assign momenta to all lines (internal and external), write down the spinor/polarization factors for external lines, write the propagators for internal lines, include the vertex factor -ie gammamu at each vertex, impose momentum conservation at each vertex, and multiply everything together. For processes with identical external fermions, include a relative minus sign between diagrams related by exchange of two external fermion lines.
The remarkable fact about QED is how much physics follows from this one vertex. The Coulomb force, the Lamb shift, the anomalous magnetic moment of the electron, pair production, Compton scattering, Bremsstrahlung -- all are consequences of a single coupling. The precision of QED predictions (the electron g-2 agrees with experiment to better than one part in 1012) validates the framework of perturbative quantum field theory to an extraordinary degree. QED serves as the template for all gauge theories, including the weak and strong interactions.