Abstract:We often use "explainable" Artificial Intelligence (XAI)" and "interpretable AI (IAI)" interchangeably when we apply various XAI tools for a given dataset to explain the reasons that underpin machine learning (ML) outputs. However, these notions can sometimes be confusing because interpretation often has a subjective connotation, while explanations lean towards objective facts. We argue that XAI is a subset of IAI. The concept of IAI is beyond the sphere of a dataset. It includes the domain of a mindset. At the core of this ambiguity is the duality of reasons, in which we can reason either outwards or inwards. When directed outwards, we want the reasons to make sense through the laws of nature. When turned inwards, we want the reasons to be happy, guided by the laws of the heart. While XAI and IAI share reason as the common notion for the goal of transparency, clarity, fairness, reliability, and accountability in the context of ethical AI and trustworthy AI (TAI), their differences lie in that XAI emphasizes the post-hoc analysis of a dataset, and IAI requires a priori mindset of abstraction. This hypothesis can be proved by empirical experiments based on an open dataset and harnessed by High-Performance Computing (HPC). The demarcation of XAI and IAI is indispensable because it would be impossible to determine regulatory policies for many AI applications, especially in healthcare, human resources, banking, and finance. We aim to clarify these notions and lay the foundation of XAI, IAI, EAI, and TAI for many practitioners and policymakers in future AI applications and research.