Spin relaxation is one of the most fundamental concepts in magnetic resonance and is one of the key NMR "observables" providing critical motional information in chemical systems and, by extension, diagnostic information in clinical imaging. Yet, it can be difficult to find accurate conceptual descriptions of the two relaxation processes-longitudinal and transverse-in the NMR or MRI literature that explain why these processes are also referred to as "spin-lattice" and "spin-spin" relaxation, respectively. Often, the explanations provided in terms of energy levels, energy exchange, and the loss of phase coherence are inaccurate oversimplifications of quantum mechanical concepts and are thus incomplete and, at times, even contradictory. In fact, various texts still follow the terminology proposed >7 decades ago largely based on the theory of NMR in solids, even though it is clearly inadequate in the case of solution-state NMR. Here, we present the fundamental and quantum mechanical explanations of both relaxation processes in simple terms while clarifying and discussing the potential origins of some common confusions, nuances in the terminology, and seemingly contradictory definitions and explanations in the literature. Considering the issues with the old and inaccurate terminology, the consistent use of an alternate and more generally applicable terminology is proposed.