Musk : Coming from a glandular secretion of the male Tibetan musk deer (Moschus moschiferus L), this was considered an aphrodisiac (as well as a spiritual fragrance in the Muslim world) in the past. It also fixes and balances a composition , refining it in the most plesasurable and sensuous way. The practice of extracting the musk from the deer however is very difficult , therefore the deer was killed in the process , rendering the practice nowadays extinct. (According to Christopher Brosius however , there are currently ways of extracting it without harming the deer being examined ,which could bring back the practice of using real musk).
Synthetic substitutes came to the rescue. According to Jellineck it was Albert Baur, searching for new explosives in 1893, who noticed that the product of reaction of trinitrotoluene (TNT) and tert-butyl halides smelled pleasantly."Musk Baur" became the first synthetic musk, founding the appropriately named nitro-musks group. The second synthetic musk came out in 1894 : Musk Ketone, resembling natural musk fairly closely. From then on they were used both in perfumery and cleaning products due to their high hydrophobicity that made them stick to fabric, hence the association of many musks with "clean" smells.
However due to recent concerns about the safety of nitro musks that were used widely in functional products (remnants of which are detectable even in breast milk and in the environment of fish ), these have now been removed from commercial perfumes. The nitro musks (Musk Xylol, Musk Ketone, Musk Tibetene, Musk Ambrette, Moskene) gave a warm effect with a slightly powdery note of animalic tone. Musk ketone was widely used in the production of Chanel#5 , as well as in men's Brut and many more ,as mentioned in the Greenpeace charts of harmful musks , but happily is not used any longer.
Each category and kind of musk has a slightly different odour profile , roughly falling in either "animalic" ( raw sweat and skin smell , notably in SL Musks Kublai-Khan ) or "white/clean" musk . These latter ones smell of fresh ,clean skin and also a bit of blackberry, ambrette or ambergris and are used in numerous modern compositions ,such as in SL Clair de Musk or TBS White Musk. Fixolide, Habanolide, Galaxolide and Ambrettolide are particularly worthy of mention.
Synthetic musks are named for convenience and as a trademark. Habanolide, Thibetolide, Velvione are the Givaudan trademarks , short for longer chemical formulas ,for example. Galaxolide is IFF's name for hexahydro-4,6,6,7,8,8-hexamethyl cyclopenta-#-2-benzopyran. Surely it's easier to remember the short name! However sometimes the same formula may yield different names across different companies. It's a perplexing matter.
The polycyclic musks (Phantolide, Celestolide, Traesolide, Tonalide, Galaxolide- which smells powdery and is used mainly in White Linen as well as Tresor), as well the macrocyclic musks (Habanolide and Globalide- which smell radiantly fresh , cottony clean and metallic and sometimes called "white musks" in contrast to darker , balmier ones - as well as Thibetolide and Velvione -infamously used in Helmut Lang's Velviona almost solely) have risen as the new musks to be used in perfumery since 1979. Modern musks such as Helvetolide( which smells a bit fruity), Nirvanolide, and Muscenone are also enjoying popularity , giving their warm, inviting character to a composition.
Another matter that is tied to musks is "musk anosmia" , an inability of the subject to smell certain musks , which is not unheard of even in perfumery circles , so trying musk fragrances before buying is of paramount importance. A Google search is useful if concerned, since the space here is limited.