What’s the difference? In a word, nothing. Narcissus is the Latin name for all daffodils; all daffodils are Narcissus.
Though few do well along the Gulf Coast (Tete a Tete, jonquillas, and paperwhites are best to start with), most are perfectly hardy in the ground as perennials. I have over two dozen different varieties that have been blooming for years in my garden that came from my great-grandmother’s garden, planted the back in the 1930s.
They are best planted in the fall, or soon after their foliage dies down in the spring. Because they form flower buds for the following year after they finish flowering in the spring, it’s important to let them finish flowering and give them at least five or six weeks, or for their leaves to turn yellow, before cutting and neatening old foliage; otherwise they may skip a year or more before flowering again.
Here are some of my great-grandmother’s bulbs blooming in my garden: