The variation of heart rate in phase with breathing, known as 'respiratory sinus arrhythmia' (RSA), is a physiological phenomenon present in all air-breathing vertebrates. RSA arises from the interaction of several physiological mechanisms but is primarily mediated by rhythmic changes in cardiac parasympathetic (vagal) activity, increasing heart rate during inspiration and decreasing heart rate during expiration. RSA amplitude is an indicator of autonomic and cardiac health; RSA is diminished or absent in common pathological conditions such as chronic heart failure and hypertension. In this Expert Recommendation, we argue that the term 'RSA', although historically important, is semantically inaccurate and carries misleading pathological connotations, contributing to misunderstanding and misinterpretation of the origin and the physiological importance of the phenomenon. We propose replacing 'RSA' with the term 'respiratory heart rate variability' (RespHRV), which avoids pathological connotations and emphasizes the specific respiratory contribution to heart rate variability. We clarify that RespHRV encompasses respiratory-related heart rate variations in both the low-frequency and high-frequency bands traditionally defined in heart rate variability analysis, and that its amplitude should not be misconstrued as a measure of vagal tone. Adopting the proposed term 'RespHRV' is expected to unify understanding and stimulate further experimental and clinical research into the physiological mechanisms and functional importance of this phenomenon.