* Continue to do: This emphasizes the *intention* or *decision* to continue an action. It suggests a conscious choice to persevere. It often implies a more formal or deliberate continuation.
* Continue doing: This emphasizes the *ongoing nature* of the action. It focuses on the uninterrupted flow of the activity. It's often more concise and informal.
Here's an example to illustrate the difference:
* "He continued to struggle with the problem." This highlights the fact that he *made a conscious effort* to keep working on the problem, even though it was difficult. It emphasizes the effort and the will to persist.
* "He continued struggling with the problem." This emphasizes the *uninterrupted nature* of his struggle. The focus is on the ongoing, perhaps even relentless, nature of his difficulty. It suggests a less deliberate, more automatic continuation.
In many cases, the difference is subtle and both phrases are grammatically correct and convey a similar meaning. The choice often depends on the desired emphasis and the overall style of writing.