This question seems to come down to just a basic question of terminology.
I recognize that people often say things like "corrections to the cross section" but this is phraseology is a bit sloppy, I guess, and may cause confusion.
What that phrase really means is "corrections to a less accurate approximation of the cross section."
The universe doesn't make approximations, so the observed cross section is the true cross section and there can be no "corrections" to it.
However, we aren't capable of computing the exact cross section. We always have to make some approximations. There are various approximations that are commonly made.
First, if you imagine taking the Taylor expansion of the exact cross section in terms of the coupling constant(s), we only compute up to some order in that expansion. The lowest order corresponds to Feynman diagrams with no loops, or "tree level" diagrams. For important processes that are to be measured in an experiment, a lot of effort goes in to computing further terms in that expansion, which diagramatically corresponds to adding loops to the tree level diagrams. These loop diagrams are corrections to the tree level calculation that make the result closer to (but still not exactly equal to) the true cross section. Again, they are not "corrections" to the true cross section, which would obviously be a meaningless thing to say.
The other issue that requires approximation is that if we want to measure the production of, say, a certain B meson at an experiment, we can never force the scattering process to produce only that B meson and nothing else. In general, when we detect a B meson there will also be any number of other particles that were also produced in the same interaction. So the total cross section for B meson production is the sum of $\sigma_B + \sigma_{B, X} + \sigma_{B, X, Y}+\dots$ where $X,Y,\dots$ are anything else. These other things could be initial or final state radiation (extra gauge bosons coming off the initial or final particles), other baryons from the hard scattering, etc. In practice, it's only feasible to compute the cross section including up to some finite number of extra particles. Including these extra particles is again a correction to the no-extra-particle approximation that corrects our calculation to be closer to the true total cross section that includes all possible additions.
As a final comment, these two kinds of corrections (loops and extra radiation) are actually not independent of each other. They are intimately related and one needs to do both to get consistent results due to an issue known as infrared divergences. I won't get into that here, but it's something you can read about another time.
