Move Minutes tracks all of your activity, no matter what gets you moving. Your watch's accelerometer will continue to show your step count, but now it will also calculate the collective number of minutes you spend in motion during the day.
Heart Points gives you credit for activities that get your heart pumping harder. Your watch's accelerometer can also identify the difference between light and intense activity. Google Fit will award a Heart Point for each Move Minute that your watch identifies as moderately intense activity, and 2 points for highly intense activity. It is not based on heart rate readings.