Grade beams are usually connecting columns at the ground level to carry the ground floor partitions, so they are not considered part of foundations. However, sometimes footing are connected by "tie beams" for different reasons. These tie beams are considered part of foundations.
In my oppinion grade or tie beams should only be considered as equalizer of the deformations and elements that ensure the collaboration of the structure. They are not to be considered to transfer stresses from the structure to the earth bed. They are usually assumed to be subjected to axial force only, unless they are considered a part of a frame structure which is entirely diferent case.
I think If a full scale test can be performed than the influence of Grade beam can be physically understood, though in design or analysis the Grade beam is not considered as a part of foundation.
Correct me if I'm wrong, but I think it is not important what do we call these elements. A grade beam, whatever it is, is a part of the structure which should contribute to provide a safe load path for the whole structure. In some structural systems, such as SMRF, grade beams supposed to provide kind of lateral brace for different parts of the foundation. But in some other structural systems, such as steel shear walls, the grade beam under the steel wall would experience large demands and it should pass more specifications.
So columns, beams, slabs, foundations, soil, etc. are all nothing but some connected hooks which should provide some safe paths to transmit all forces to deep layers of ground.
Strictly speaking, we can call a grade beam "cell phone", "hammer", or whatever we want....! In any case, it should be proportioned (designed) according to a well understood procedure.
The answer to this question depends on the level of accuracy of analysis and design expected. But, in a more real structural modeling, the grade beam is clearly play a significant effect on the structural behavior and should be analyzed as a structural component (foundation). For example, the brick wall that is held above the grade beam impact quite significantly on the behavior of the columns of the building and causing an increase in bending moment and shear force.
Really, I try to find clear answer about it (it is not my area of research. In any way the tie beam (grade beam) which is connecting the foundation and it is bottom level same as the foundation bottom level. As a rule of thumb from 30 years we design it to carry the wall load as a beam and put the same steel amount upper and lower. My concern why the soil bearing capacity is not considered. at least i try to find code or standard cover. I found one reference mention that its width should be the span /20. if it can carry differntial settlement what is the amount it can carry. based on this scenario. If any one have any reference let me know. as it is very simple but need more digging.