I was wondering the other day about the difference between these two words.

Problem:
These two adverbs are not synonyms (except in sloppy speech or writing).

Explanation:
The adverb “continually” means at frequent or regular intervals.

The adverb “continuously” means without cessation, or uninterrupted in time.

In other words, “continually” applies to events, whereas “continuously” applies to processes.

Solution:
Use “continually” when talking about an event that occurs frequently or regularly. Use “continuously” when talking about a process that does not stop.