Is your heart rate and pulse rate the same thing?

Heart rate: Heart rate and pulse rate usually are the same. They can differ if not all cardiac depolarizations result in a pulse being conducted to the extremities where it can be sensed or recorded.

Usually yes: Heart rate is how often your heart is beating. Pulse rate is the detection of this beat at another point in your body (arm. Groin, neck, etc.). If heart is beating weakly or irregularly, the weaker beats may not be detectable in the part of the body where the pulse is being checked, and this could cause a difference. A blood clot to the area being checked could also block detection of pulse.