Under normal circumstances, both are the same.
Very simply, your heart rate
is the number of times your heart beats per minute. You can measure your heart rate by feeling your pulse - the rhythmic expansion and contraction (or throbbing) of an artery
as blood is forced through it by the regular contractions of the heart. It is a measure of how hard your heart is working.
Your pulse can be felt at the wrist, neck, groin or top of the foot - areas where the artery is close to the skin. Most commonly, people measure their pulse in their wrist. This is called the radial pulse.