Terry, "They continue smoking" vs "They continue to smoke" is a difference of tenses. The first is present continuous, and the second is present simple. I recommend studying English verb conjugations to recognise them when you see them.

No difference but "they continue to smoke" is more common.

Hi, the tense difference indicates different situations, i.e. 'they continue smoking' means they have been smoking and they are still smoking right now, whereas 'they continue to smoke' could mean that the people being referred to are smoking right now, but in most usual sentence constructions would mean that they have not given up the habit of smoking, but they may or may not be smoking right now. Some examples of usual usage might help: I talk to the people standing outside the building, smoking. I walk away, they continue smoking (i.e. they were smoking and are still smoking right now) Despite being informed that smoking will further damage their health, they continue to smoke (i.e. these people have not given up smoking, but may or may not be smoking right now)