There is no big difference between Caulk and silicone in that, the two are examples of fillers used to make joints or seams against leakage in various piping and structures. Many people confuse the two because their functions are quite similar. They are used for the same purpose but the difference between the two lies in the manner they are used and which of the two fillers to be used.
The main difference between caulk and silicone is the elasticity which means one is more elastic than the other. Silicone is an elastic material which can be used to fill cracks or gaps between building materials. While caulk is more rigid when dry and is used to fill cracks in area with less expansion and contraction. Another difference is that, caulks are paintable i.e. you can apply paint on them and you can easily clean them with water, while silicones are not paintable and their smears are cleaned up with solvents