I’m pretty much certain that this was not what you were getting at, but there are, indeed, circumstances where the heart beat and “the pulse” have different values.
In one extreme example, a person’s heart may be beating so ineffectively, or the blood pressure may be so low (due to, say, blood loss) that each beat of the heart is ineffective in producing a palpable (i.e. ‘feelable’) pulse at the wrist or wherever. And, note that the heart beat itself in such circumstances is still easily audible in the chest by using a stethoscope. By the way, this phenomenon leads to the general rule that if you can’t feel the pulse at the wrist, then the (systolic) blood pressure is less than 80. Can’t feel it the neck? Then the BP is less than 60.
A less alarming situation where the beat of the heart doesn’t match the beat as felt and counted at the wrist can occur in the very common condition known as atrial fibrillation. In atrial fibrillation, the priming chamber (atrium) of the heart is not contracting in a coordinated manner and, as well, the electrical impulses traveling from the priming chamber to the main pumping chamber (ventricle) arrive at the latter randomly. The net effect can be for the heart to beat at an irregular rate with only some of those beats powerful enough to create a palpable impulse (i.e. “a pulse”) at the wrist. So, for example, listening over the chest with a stethoscope may reveal a heart rate of 100, but the rate as counted at the wrist could be 60. That is called a ‘pulse deficit’. If anyone’s interested I can elaborate on the mechanism for this occurrence.