再次 and 再: are they different?
The answer by  Camila Ting Chen is close. We don't use 再次 in an present active sentence. We use 再次 with some perfectness or passiveness. Such passiveness is not necessarily related to the conjunctive 被 however. A simple rule is when we can say 再 alone, say it alone.

我再次来到这家餐厅。

我时隔数年再次遇到一位朋友。

这盘菜再次被我吃掉了。 while this sentence is not logical at a first glace, it sound good in this specific situation.