To do and doing means the same. The difference is in grammar, when to use it and how to use it.

"Start to do" and "start doing" mean essentially the same thing in English. However, "start to do" (the infinitive form) is used much less than "start doing" (gerund) in acual practice.

he stops to smoke----he wanted to smoke so he stopped something he stops smoking---he doesn't smoke just now or he's not smoker now. i remember like these.