The horticultural classifications and descriptions are hard to come by because there are not may definitive sources for this information. I have tried my best to come up with the classifications of many of the hardy Sedum that we offer.

Family Crassulaceae

Genus Sedum

Genus Sedum subgenus Sedum

• Growth completely dies back to ground in winter
• Leaves are flat, toothed near the tip.
• Rootstocks are thick and woody
• Flowers are yellow to rich orange, flowering in midsummer

• Sedum ellacombianum (Russian Stonecrop)
  Leaves of this species are vibrant green, forming a dense carpet on 4 inches high with bright orange fruit. It is a vigorus ground cover, not minding a bit to trail over adjecent edges, rocks, steps or paving, "very eye-catcatching as they take on the shpe of whatever they engulf". Though a vigorus groundcover, it is easily controlled and should not be considered a pest.
• Sedum kamtschaticum (Russian Stonecrop)
  See Sedum ellacombianum as a preferred alternative for this form, for better foliage look and color.
• Sedum kamtschaticum 'Variegatum' (Variegated Russian Stonecrop)
  This form is a delightful, slow-growing, with almost entire leaves edged in cream. Leaf margins are blushed orange or pink in full sun giving the leaves a tricolored effect. Flowers of this variety are large, approximately 3/4" across, deep yellow, fading to orange.

(European - Yellow Flowered Orthocarpic Group)

• Sedum rupestre 'Angelina' PPAF (Blue Spruce Stonecrop)
  This form is a short (3-5") but sturdy upright plant with tall inflorescences. It is an agressive ground cover but not unruly. An excellent choice for any difficult spot in the garden. It grows well on a wall and often seeds itself around. Golden-yellow evergreen, needle-like foliage. In colder months the tips of the leaves take on a reddish-orange tinge. Yellow Flowers.

(European - Non Yellow Flowered Orthocarpic Group)

• Sedum spurium
  In its numerous forms, Sedum spurium is the most common stonecrop in cultivation, usually used for rapid groundcover. Leaves are large, flat, with a creeping habit, and evergreen. Dark or variegated forms of Sedum spurium are slower growers, and together make a good foliage contrasting plants.

Genus Sedum subgenus Hylotelephium

Some members of the subgenus Hylotelephium were considered to hold magical powers since cut flowers stems can stay alive for weeks. Characteristics of this subgenus are listed.
Rootstock is fleshy or woody, sometimes protruding above the ground.
Growth completely dies back to ground in winter.
Rootstock is without thin, scalelike leaves.
Leaves are flat, spurless (no projection on the heel of the leaf), arranged along the stem.
Inflorescences are compact, terminal (orginate from growing step as opposed to the side), showing flower colors of purple, pink, white, green or cream, never yellow.
Flowers are usually 5-partite

(Hylotelephium Group)
This group will have erect stems and well-developed rootstocks.

• Sedum spectabile
  Known as the common 'ice plant' of cottage gardens, with very light bluish green leaves. This plant makes a handsome bright accent to the border. Large, flat-topped, pink-purple inflorescenses adorn the plant in autumn. The flowers are a great attraction to nectar-feeding insects, especially butterflies. Leaves are also sparsely toothed.
• Sedum spectabile 'Pink Chablis' PPAF
• Sedum telephium 'Autumn Joy' (a.k.a Sedum 'Herbstfreude', Sedum 'Indian Chief')
  Being extremely easy to grow, it is prized for its huge inflorescenses of convex, compact purple or rust-colored flowers in autumn, atracting butterflies. This form is sterile (no male parts), thus plants are always cloned from vegetative propagations. Leaves are blue-green, extremely toothed. As the leaves rise up on the stems, the become much smaller and have a different shape. In rich soil plants can reach heights of 3 feet! Flowers can be cut and dried artificially in flower arrangements. The flower head after drying can be dyed or painted. The dried flowers are long-lasting and tend not to break up because the plant is sterile.

(Populisedum Group)
This group lacks 'well-developed' underground rootstocks, and flowering stems rise only from persistent nodes on the bases of last year's flowering stems.

• Sedum cauticola
  Plants for a loose carpet of particially erect stems about 5 inches long, with leaves attached opposite each other on the stem, colored powdered-gray/blue heavily spotted with purple. Sedum cauticola and it's forms do best in well drained gardens, ideal for raised beds and containers, highlights light colors rocks.
• Sedum cauticola 'Bertram Anderson'
  Similar to Sedum cauticola but more upright and very branched.
• Sedum cauticola 'Lidakense'
  Most common form in cultivation with small egg shapped leaves. Very good soil coverage.

(Sieboldii Group)
This group has stems that creep then rise or hang. Rootstocks are well-developed.

• Sedum sieboldii
  A very diverse use Sedum, it can be used in rock gardens, potted house plants and even hanging baskets. Long arching stems produce progressively smaller leaves at they tend toward the tip. Leave are not particularly succulend, are bluish-gray, and almost round and group in threes, toothed on the upper half. Outdoor plants tend to be more colorful, and also have teh additional feature of blushing with red in summer. Pink flowers appear in October. Non-variegated shoots should be removed from the parent plant because their vigorous growth will cause the whole plant to revert.