Our computer programs execute logic, but cannot reason about it. Reasoning is the ability to dynamically consider constraints we've never seen before and then determine how those constraints would lead to a final conclusion. The rules of mathematics we follow are not programmed into our DNA; we learn them and follow them while our human-programming is actively running. But we can just as easily, at any point, make up new constraints and follow them to new conclusions. What if 1 + 2 is 2 and 1 + 3 is 3? Then we can reason that under these constraints we just made up, 1 + 4 is 4, without ever having been programmed to consider these rules.

Executing logic is deductive reasoning. But, yes, I get it. There are also other layers of reasoning, and other forms. For instance, abductive and inductive inference.