What is the physical interpretation of the two tree-level Feynman diagrams for $e^-e^- \to e^-e^-$ scattering? In the tree level, the  $e^-e^- \to e^-e^-$ scattering has two Feynman diagrams, the first one is indicative that one electron emitted a photon which was later absorbed by the other electron:

However, I have yet to understand how we can interpret the other term:

at first glance it would seem like the electrons changed places or simply that they have opposite 4-momentum compared to the previous diagram, but I am still not sure what is the correct interpretations.
 A: It is precisely what you said. When you do a scattering experiment, you're throwing in two electrons with momenta $p_1$ and $p_2$ and see two electrons coming out with momenta $q_1$ and $q_2$. However, electrons are indistinguishable, so you can't know whether the electron with momentum $p_1$ is the one with momentum $q_1$ or the one with momentum $q_2$ (to be fair, due to indistinguishability, the question doesn't even make that much sense). The first diagram can be thought of as pictorially describing the case in which $p_1$ becomes $q_1$ and $p_2$ becomes $q_2$, while the second diagram describes the possibility of $p_1$ becoming $q_2$ and $p_2$ becoming $q_1$.
It should be remarked that Feynman diagrams should not be taken too literally. They are mainly just computational tools and interpreting as what actually, physically happens is an extra philosophical step. The surely provide a pictorial interpretation, but it is important to recall that there is nothing ensuring that is what actually happens. Some physicists do prefer to interpret it like that, it is important to notice this is an extra philosophical step (just like choosing to interpret as something with no physical meaning).
Also, while splitting the two diagrams is necessary in the computation and this allows the interpretations I explained in the first paragraph, it is important to recall electrons are indistinguishable, so there's no really way of saying (or even asking) where the electron $p_1$ turned into $q_1$ or not.
