The difference between interaction and reaction cross-sections is that the reaction cross-sections include the cross-sections of all processes except of the elastic scattering, whereas the interaction cross-sections do not include the elastic scattering as well as the processes with a target nuclei excitation or disintegration. Usually this difference is neglected in the analyses of experimental data.
The question makes sense. Indeed, the chemical reaction actually have interaction. In physics, for example, in reaction to the action of the photon the atom has a different photon radiation. As you can see, "reaction" is a special case of "interaction".
A gauge boson (say, a photon) may be radiated from a proton.
Or another boson (a W) may be given off from a u/d reaction.
If the event leaves the original parts unchanged, that's probably best called an interaction. If there are non-trivial changes then 'reaction' may be the best description.
The difference between interaction and reaction cross-sections is that the reaction cross-sections include the cross-sections of all processes except of the elastic scattering, whereas the interaction cross-sections do not include the elastic scattering as well as the processes with a target nuclei excitation or disintegration. Usually this difference is neglected in the analyses of experimental data.
When talking about nuclear physics interactions are considered the ways in which actions take place between the various parties involved, namely the types of forces acting between nucleons and between elementary particles in general.
When talking about nuclear reactions are considered the collision processes involving nuclei, nuclei and particles or particles and particles. Obviously, during a nuclear reaction the nuclear interactions are at work!
Nuclear species can be transformed in a multitude of nuclear reactions, such as neutron adding or nockout reaction, as a result of this reaction we get a new isotope. In nuclear reactions involving only strong and electromagnetic interactions ,the number of protons and neutrons are conserved separately.
The interaction is describe the force between electrons and nuclei or between nucleons in the same nucleus. Force between nucleons are neither simple nor fully understood. One of the reason for this is that the interactions between nucleons are "residuals" or of the fundamental interaction between quarks inside the nucleon. In that sence, the nuclear interactions are similar to Van der Waals forces between atoms or molecules
Interaction is something that changes the state of motion of a particle when it is close to another particle, without changing its internal structure. Like we have four basic interactions, strong, weak, electromagnetic and gravitational. When the two interacting particles change their structure (split, excite, absorb another particle) then the process is a reaction. Usually, reactions are caused by interactions and they occur in composite particles (like nuclei). But this last thing is somewhat loose in case of particle physics where particles can be created and annihilated.
I think interaction is more of a general term. When we are not specific about a reaction we use interaction(s). On the other hand we can use reaction to address any specific interaction that non-trivial changes happen after interaction(collision) like fission or fusion or inelastic scattering...