They both can mean " 就是”,which means " it is " in English . While “便是”can also mean “即使，纵然”，which means " even though" in English .for example : 便是皇帝来了，我也不怕。besides, you can use " 便是” in a conditional situation to express a wish ，你若安好，便是晴天。which is equal to " if ..then .."。 "正是“ is used when you are 100% sure about your saying ,which means " exactly " in English