difference in continuity

my mom found a difference between continual and continuous.  they both meant something unbroken in a rough sense.  but continuous is really in a chain without a stop, continual meant something keep occurring, but  with intervals in between.  the example they used in the 世界週刊, is raining.

if the rain has been pouring in the past few days, you may say there were rains pouring continually these few days.  this meant that there were rains, but there were also times with no rains.  if we replaced the word with continuously, then there's no intervals.  the rain never stopped pouring.

tedious knowledge...  but interesting...