Originally a small vase used for display of specimen flowers. Sir Joseph Banks believed to have used the word in his Florilegium compiling the botanical works of many of his peers from the 1700's. The word has more recently taken on a broader meaning, pertaining to any size vase containing flowers arranged within the vase. This being a distinction from a bouquet, arranged within the hand, then tied with ribbon and bow, (often wrapped in paper, cello or other materials) and then placed in a vase.
1/. The hotel manager requests a large vasette to be placed at the entry to the foyer. I suggest 5 foot high blossom to support the orchids and lilies.
2/. Place a vasette with a single peonie on my desk please.