It's still unclear what you mean. One simple idea is that many formalisms allow to express each other, but some give more natural ways of representing a given problem than others. In some contexts, a given way of stating things may be clearly superior. If you e.g. see math as something happening in heads of mathematicians, or see implication of classical logic as a certain idealization of material implication where nothing changes, one may argue that a given way is more fundamental, closer to what actually happens.

When you ask questions like "do you see it now?", I doubt there is even a good way of interpreting them as having definite answers, without already knowing what you expect to hear, a lot more context about what kinds of things you are thinking about than is generally available.