Are there really any differences between "continue to do something" and "continue doing something"?
I found there are some different ideas from English experts that if there are really any differences between "continue to do something" and "continue doing something". Kindly let me know. Thank you!

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I tried out a few sentences in my head and the meaning sounded the same in both cases.  "To continue" is therefore a verb in the category of verbs which can be followed either by an infinitive or a gerund.

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I don't think that there is any difference in meaning.

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This is indeed the same. -ing means that you are in the process (I'm eating a pizza - right now)