I used to distinguish the two words in this way:
In my imagination "continual" is more like "frequent". It means many times but with pauses or breaks in between.
"Continuous", on the other hand, conveys a sense which is closer to "constant", I imagine.
Let me use an example.
The phone rang continually all through the day.
یعنی تلفن تمام روز بارها زنگ خورد
The alarm sounded continuously for a whole half hour or so.
آژیر برای مدت نیمساعت کامل یا این حدود صدا داد.
In the first sentence the ringing is said to occur many times during the day.
In the second sentence the sound of the alarm just didn't stop at all.