I am really amazed at the number of varieties of daffodils there are in the world. Apparently, this is one type of flower that can have a lot of hybrids. All of them are in the genus of narcissus in the Amaryllis family. Depending on your source, there are as many as 60 species of narcissus, all of which I would probably call daffodils. Other common names are jonquil and, of course, narcissus.