Difference between a daffodil and a narcissus

There is no difference between daffodil and narcissus. The botanical name narcissus is used for both plants. The separation into narcissus and daffodil is an entirely artificial one that has been created by gardeners. Gardeners tend to use the name daffodil for narcissi with long trumpets. When they talk about narcissi, they are referring to flowers with short, cup-like trumpets.

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Daffodil

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Narcissus