The distinction between reason and proof lies in their nature and function within the realm of knowledge and understanding.

1. **Reasoning**: Reasoning involves the process of using logical thinking, intuition, and inference to arrive at conclusions or make sense of ideas. It often involves the application of principles, rules, or cognitive abilities to reach a justified belief or decision. Reasoning can be deductive (drawing specific conclusions from general principles) or inductive (drawing general conclusions from specific observations). It is essentially the mental activity of making sense of information or arguments.

2. **Proof**: Proof, on the other hand, refers to providing evidence or demonstrating the validity of a claim or assertion. It involves presenting empirical data, logical arguments, experiments, or other forms of evidence to substantiate a statement or to establish the truth of a proposition. Proof is typically more concrete and objective than reasoning because it aims to validate claims using verifiable methods or facts.

The key difference between reasoning and proof is that reasoning is the process of thinking or mental activity that leads to understanding or belief, while proof is the presentation of evidence or justification that supports a claim or conclusion. In essence, reasoning is the cognitive process, whereas proof is the tangible or demonstrable support for a claim. While reasoning can lead to hypotheses or theories, proof is what validates these ideas through empirical or logical validation.

Therefore, reason and proof complement each other in the pursuit of knowledge and understanding. Reasoning helps formulate ideas and hypotheses, while proof provides the necessary evidence or validation to substantiate these ideas. They are distinct aspects of intellectual inquiry, each playing a crucial role in the development and validation of knowledge.