The Basic Daffodil Dictionary.

Corona refers to the cup or the trumpet.

Perianth refers to the petals.

Reflexed petals are those which are angled away from the corona.

Pedicel is the ‘neck’  of flower which joins it to the stem.

Horticultural Classifications of Daffodils

Daffodils are divided into 13 divisions, based mainly on flower form, and these divisions are often referred to in bulb catalogues. Some divisions are known particularly for their fragrance, or for their ability to naturalise in grass. A brief summary is given in the photo gallery below.

Division 1. Trumpet.
One flower per stem; longer corona (trumpet) at least  as long as the perianth segments(petals).
Division 2. Large Cupped.
One flower per stem; shorter corona (cup) is more than one third but less than equal to the length of the perianth segments (petals).
Division 3. Small Cupped.
One flower per stem; corona (cup) not more than one third the length of the perianth segments (petals)
Division 4. Double.
One or more flowers per stem; double the numbers of perianth segments or the corona or both.
Division 5. Triandrus.
Usually two or more pendant flowers per stem, perianth segments often reflexed.
Division 6. Cyclamineus.
One flower per stem;perianth segments prominently reflexed. Flower at an acute angle to the stem  with a very short pedicol,
Division 7. Jonquilla and Apodanthus.
Usually 1 to 5 (more rarely, up to 8) flowers per stem, perianth segments reflexed or spreading, corona is cup or funnel shaped or flared, usually wider than long. Usually flagrant.
Division 8. Tazetta.
3 to 20 flowers per stem, perianth segments spreading (not reflexed) and usually flagrant.
Division 9. Poeticus.
Usually one flower per stem;perianth segments white, corona very short or disc shaped, usually with a green/yellow centre and red rim but sometimes of a single colour.
Division 10. Bulbicodium.
Usually one flower per stem; perianth segments insignificant compared to the corona; anthers dorsifixed (i.e. attached central to filament); filament, style curved.
Division 11. Split Corona.
Corona (cup or trumpet) is split, usually for more than half its length. Either with the corona segments opposite the perianth segments usually in two whorls of three (Type A), or with the corona segments alternate to the perianth segments, usually in a single whorl of 6 (Type B).

Division 12. Other.

This is for the “miscellaneous” cultivars which do not fit the other classifications.Division 13. Other.
This classification is for the cultivars distinguished solely by botanical name.