This is one of those things native speakers don't even stop to think about. Let me see... I'm continually fascinated by the birds that migrate here every winter... He is continually annoying his little brother... How long does the song play in the background? It's continuous. To be honest, I never find myself in a situation to use "continuously." OK, just looked at that article: Continually describes something that is frequently occurring but intermittent. Continuously describes something that occurs without interruption.

Hello, there is a comment here. I think it will help you. http://writingexplained.org/continually-vs-continuously-difference

Hi there! I would say: "We had an argument and stopped speaking. Later, we decided to continue our conversation talking for a very long time." "We had an argument and stopped speaking. Later, we continued our conversation for a very long time." Something like these to give you examples. Hope it helps! Keep on learning! David

Both words mean "without stopping". There are some differences in typical usage but I would not worry about them until you are an advanced speaker.

maybe you can use "continue to" in this case.