Reading the wikipedia of Bhabha scattering, I see that the electron-positron annihilation and electron-positron scattering are analyzed seperately. What are the differences between these two processes? Why aren't they the same process?
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$\begingroup$ How can annihilation be the same as scattering? After annihilation the incoming two particles no longer exist, while after scattering, they do still exist. $\endgroup$– GhosterCommented Oct 18, 2023 at 1:45
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The diagram on Wikipedia (attached below) says that an $e^-$ and $e^+$ can scatter either via an exchange of a photon (second diagram) or they can totally annihilate each other, converting their energy into photons and then be recreated from the same photons. Both these processes account for a Bhabha scattering process.
On the other hand, you can have an $e^-$ and $e^+$ that simply annihilating each other. In this case, you will only be left with energy.
