True lilies - Genus - Lilium

The most common are classified as:

 The Asiatic lilies, which are most common on the cut flower market, grow with flowers that are up-facing, out-facing and down-facing. Some have fragrance. 

Longiflorum-Asiatic ("LA") Hybrid Lilies.

Oriental lilies  Flowers are larger and often more showy in pinks and reds–the most popular 'Star Gazer' is an example. All have fragrance. 

Tigrinum lilies. Syn: The Tiger Lily. Tigrinum Lilies are hardy, floriferous and have y recurved flower petals, light to heavy maroon spotting and small, dark purple bublets at their leaf axils.

Trumpet lilies - Their flowers are large and cone shaped. Plant height up to five feet tall. 

Orienpets, the newest development, are a cross between Orientals and Trumpets, which have extreme vigor and disease resistance and can grow to seven and eight feet high. 

What about fragrance? - Yes.

The trumpets (African Queen) and Orientals (Casa Blanca)  are famous for their fragrance.

Do all true lilies bloom at the same time? - No!