What is the difference between daffodils and narcissus?
None. The two words are synonyms. Narcissus is the Latin or botanical name for all daffodils, just as ilex is for hollies. Daffodil is the common name for all members of the genus Narcissus, and its use is recommended by the ADS at all times other than in scientific writing.
What is a jonquil?
In some parts of the country any yellow daffodil is called a jonquil, usually incorrectly. As a rule, but not always, jonquil species and hybrids are characterized by several yellow flowers, strong scent, and rounded foliage. The hybrids are confined to Division 7 and the term "jonquil" should be applied only to daffodils in Division 7 or species in Division 13 known to belong to the jonquil group.
Here's a jonquil from Division 7, just for comparison. See the rounded leaves and more than one bloom per stalk. That's what causes it to be called a jonquil, although it's still a daffodil. :-)