The reason Stethoscopes have two sides to them is so that you or the doctor can hear different frequencies of sounds.
The bell side of the stethoscope which is the smaller side is used to hear lower frequency sounds while the diaphragm side which is the larger side of the stethoscope is used to hear higher frequency of sounds.
The higher frequency sounds would be your heart beat while lower frequency sounds would be your pulse.
So when a doctor checks your pulse they would likely use the bell side of the stethoscope and when checking the sound of your heart they would likely use the diaphragm side of the stethoscope.