Continue + infinitive or ing

I know there’s little difference in meaning between the two structures: continue to do or continue doing. I came across the suggestion we normally use continue to when we are talking about a state, as opposed to an action. Is this correct or would the diffence be another one? Thank you

What I know is that “go on” which means the same is used with gerund when we cotinue what we have been doing,go on to is used when we start smth esle.
For instance
When I entered the foom she was reading a book,she greated me and went on reading.
After succeeding in writing historical novels she went on to write about her life.

I agree: We continue doing the same and continue to do (e.g. somebody continued his/her speech) something else