Continuously describes an ongoing action that happens without ever stopping. Continually describes an action that happens often or regularly, but not continuously.

I don't know. Good question even for a native speaker.

They’ve been in business for 80 years. They’ve been in business continuously for 80 years. (Without a break. Not ‘continually’) He makes fun of my accent. He continually makes fun of my accent. (Repeatedly, regularly. Not ‘continuously’) In some cases, you might hear ‘continuously’ to indicate the second meaning. That could be a deliberate exaggeration, or it could be a mistake.

Continuously describes an action that happens without ceasing(不停地eg They chattered continuously for an hour and continually describes an action that recurs frequently(频繁地) eg They are continually late to class.