I'd wager that most native speakers would have to look up both words in the dictionary. I did for the second one. Unless you want to sound really fancy, don't use these words. ;) Use "procrastinate" instead of "shilly-shally." And instead of "Bob is trying to decide what to order for lunch but he's vacillating [about it]" use "Bob is trying to decide what to order for lunch but he can't make up his mind."

To vacillate is to be unable to make up your mind or decide. It does not mean procrastinate. http://www.ldoceonline.com/dictionary/vacillate Shilly shally is can mean vacillate, but can also mean procrastinate. If you shilly shally, you waste time in coming to a decision, either by being unable to decide, or by putting off making a decision. Examples: We want to go on a cruise but we can't decide where. We keep vacillating between a trip to the Caribbean and a European cruise. If you don't stop shilly-shallying around about what movie you want see, it will be too late to go.

Hi Weiyang Luo: "Shilly-Shally" is a common expression which refers to the kind of imprecise, purposeless, BACK---AND---FORTHING in human experience which accomplishes nothing. Examples: #1 A great many topics in the Italki "Discussion" forums consist of little more than a kind of Shilly-Shallying around. #2 "When you are done with this kind of Shilly-Shallying around, let me know, because I have work for you to do." #3 "If all you can do is just Shilly-Shally around, then I want nothing to do with you. I have business to conduct here." #4: "Knock of the Shilly-Shally attitude and get to the point!" ---------------------------------------------------------- To Vacillate is to be indecisive. It can be used in the same sense as the colloquialism or idiomatic expression Shilly-Shally, but it does not mean exactly the same thing. Vacillate is a literalism. It means to be involved in some sort of decision-making process, in which one minute one might choose to do something, but the next minute, decide not to do anything at all. Vacillation is not exactly " Shilly-Shallying around" but it could be. Shilly-Shally refers to silly or foolish or wasteful activity. To Vacillate, is to have difficulty making up one's mind, as follows: #1 I tend to vacillate about my financial choices. I cannot make up my mind to buy a new car now, or to wait another year. #2 The Student vacillated between asking the Italki Teacher for lessons, or choosing to study English independent of a teacher. #3 The Military Council had little time to vacillate. A serious decision had to be made about whether to take military action, or to use diplomacy.