Sinus arrhythmia: The normal increase in heart rate that occurs during inspiration (when you breathe in). This is a natural response and is more accentuated in children than adults.
The "sinus" refers to the natural pacemaker of the heart which is called the sinoatrial (or sinus) node. It is located in the wall of the right atrium (the right upper chamber of the heart). Normal cardiac impulses start there and are transmitted to the atria and down to the ventricles (the lower chambers of the heart).
Sinus tachycardia refers to a fast heartbeat (tachycardia) because of rapid firing of the sinoatrial (sinus) node. This occurs in response to exercise, exertion, excitement, pain, fever, excessive thyroid hormone, low blood oxygen (hypoxia), stimulant drugs (such as caffeine), etc.
The lack of normal sinus rhythm is an arrhythmia, an abnormal heart rhythm.