I do not understand how the diagrams for t and u channel processes given on wikipedia are different, and why it is meaningful to list them. Below are the two processes I reference:
It seems to me that, just as these two diagrams for compton scattering are equivalent:
And things like the angles particles make in Feynman diagrams don't matter, it shouldn't matter whatsoever if particles cross or not. What am I missing?
The dependence of the processes on the moemnta are entirely different, being roughly $$ \frac{1}{(p_2-p_4)^2 -m^2} $$ for the first and $$ \frac{1}{(p_2-p_3)^2 -m^2} $$ for the second.
Well, you are right in that the two diagrams you show for the Compton scattering are indeed equivalent. However, these are neither t- nor u-channel diagrams; the diagrams you show are s-channel diagrams.
The key point is that the first two diagrams are indeed different. The easiest way to see that is by looking at the momenta that flow into each vertex; on the left diagram we have the following:
Upper vertex: $p_1, p_3, q$
Lower vertex: $p_2, p_4, q$
(where $q$ is the momentum of the propagator)
On the other side, for the right diagram, we have
Upper vertex: $p_1, p_4, q$
Lower vertex: $p_2, p_3, q$
Therefore, since the momenta that flow in each vertex are different, the two diagrams correspond to two different scenarios and thus both need to be considered.
Compare this with the Compton diagrams that you show; in both cases, the momenta flow of each vertex are
Left vertex: $p_1, p_2, q$
Right vertex: $p_3, p_4, q$
There is a second diagram for Compton scattering; this would correspond to a $t$ channel (or $u$ channel; this depends on how you label the momenta). See if you can find it.
