Bayesian optimal interval (BOIN) design is a model-assisted phase I dose-finding design to find the maximum tolerated dose (MTD). The hallmark of the BOIN design is its concise decision rule - making the decision of dose escalation and de-escalation by simply comparing the observed dose-limiting toxicity (DLT) rate at the current dose with a pair of optimal dose escalation and de-escalation boundaries. The interval 3+3 (i3+3) design is a recently proposed algorithm-based dose-finding design based on a similar decision rule with some modifications. The similarity in the appearance of the two designs has caused confusions among practitioners. In this article, we demystify the i3+3 design by elucidating its links with the BOIN design and compare their similarities and differences, as well as pros and cons. We perform comprehensive simulation studies to compare the operating characteristics of the two designs. Our results show that, compared to the algorithm-based i3+3 design, which are characterized by ad hoc and often scientifically and logically incoherent decision rules, the mode-assisted BOIN design is not only simpler, but also statistically more rigorous with better operating characteristics, thus providing a better design choice for phase I oncology trials.