There are many types of daffodils in the world, and to keep things organized, they are all classified according one particular system;
The RHS Horticultural Classification.
Below you will and an overview of what the various divisions mean, how you can determine to which division your daffodil belongs to, and how the colour coding system works.
Division 1 - Trumpet Daffodils
One flower to a stem; corona (“trumpet”) as long as, or longer than the perianth segments (“petals”)
Division 2 - Large-Cupped Daffodils
One flower to a stem; corona (“cup”) more than one-third, but less than equal to the length of the perianth segments (“petals”)
Division 3 - Small-Cupped Daffodils
One flower to a stem; corona (“cup”) not more than one-third the length of the perianth segments (“petals”)
Division 4 - Double Daffodils
One or more flowers to a stem, with doubling of the perianth segments or the corona or both
Division 5 - Triandrus Daffodils
Characteristics of N. triandrus clearly evident: usually two or more pendent flowers to a stem; perianth segments reflexed
Division 6 - Cyclamineus Daffodils
Characteristics of N. cyclamineus clearly evident: one flower to a stem; perianth segments significantly reflexed; flower at an acute angle to the stem, with a very short pedicel (“neck”)
Division 7 - Jonquilla Daffodils
Characteristics of Sections Jonquilla clearly evident: one to five (rarely eight) flowers to a stem; perianth segments spreading or reflexed; corona cup-shaped, funnel-shaped or flared, usually wider than long; flowers usually fragrant
Division 8 - Tazetta Daffodils
Characteristics of Section Tazettae clearly evident: usually three to twenty flowers to a stout stem; perianth segments spreading not reflexed; flowers usually fragrant
Division 9 - Poeticus Daffodils
Characteristics of N. poeticus and related species clearly evident; perianth segments pure white; corona very short or disc-shaped, not more than one-fifth the length of the perianth segments; corona usually with a green and/or yellow centre and red rim, but sometimes wholly or partly of other colours; anthers usually set at two distinct levels; flowers fragrant
Division 10 - Bulbocodium Daffodils
Characteristics of Section Bulbocodium clearly evident: usually one flower to a stem; perianth segments insignificant compared with the dominant corona; anthers dorsifixed (ie attached more or less centrally to the filament); filament and style usually curved
Division 11a and 11b - Split-Corona Daffodils
a) Collar Daffodils Split-corona daffodils with the corona segments opposite the perianth segments; the corona segments usually in two whorls of three
b) Papillon Daffodils Split-corona daffodils with the corona segments alternate to the perianth segments; the corona segments usually in a single whorl of six
Division 12 - Other Daffodils
Daffodil cultivars which do not fit the definition of any other division
Division 13 - DAFFODILS DISTINGUISHED SOLELY BY BOTANICAL NAME
One flower to a stem; corona (“trumpet”) as long as, or longer than the perianth segments (“petals”)