Is there a difference between an irregular pulse & an irregular heart rate?

No, technically yes. They both indicate an irregularity of your heart's rhythm. If you listen at your chest, you actually hear the heart beats. If you check a peripheral pulse, you're feeling the momentary arterial bulge that results from the heart beat. Special case: in atrial fibrillation, the pulse rate will always be "slower" than the hr because some beats aren't transmitted.