As most musks are synthetically synthesized in the lab these days I suspect that the different musks refer to the scent character of each 'musk' blend.
Just as you can now get many synthetic blends that highlight very different aspects / characteristics / varieties of a single wood (cedar, sandal) or flower (jasmine, rose), you can do for musk also.
When browsing professional aroma and flavour chemical supplier websites I have noticed that there are always a few variants of 'musk' that are available, which have different scent signatures and chemical structures.
There are three main groups: nitro musks, polycyclic musks and macrocyclic musks. Musk xylene (a nitro musk) is a particular problem as a widespread contaminant of the environment. The polycyclic musks are thought to less environmentally-damaging than nitro musks but they are also persistent, bio-accumulative and toxic to reproduction. Macrocyclic musks are currently being investigated as possible substitutes for the other two musk groups.
Most musk scent chemicals available now are the Macrocyclic musks.
When it comes to the character of each musk scent in a perfume blend the musk type often alludes to a classic regional scent signature:
Egyptian Musk is traditionally a very light, delicate combination of clean musk, fresh citrus, and soft floral is accented by precious wood notes.
White Musk is a very soft, powdery musk to those who can smell it. This is usually combined with soft white florals and is prevalent in feminine perfumes. Many people tend to be anosmic to this type of musk.
Indian Musk tends to be animalic (see below) featuring notes of sandalwood, incence and intense florals such as jasmine and rose.
Tunisian / Tibetan Musk is aromatic and tends to feature soft florals (champac, rose) , balsams and incense.
African Musk is similar to Egyptian Musk but tends to feature a quite fresh green opening, with a smooth, 'clean' / soapy heart and a soft skin-but-better base. It can also feature a strong rose note.
China / Japanese Musk is delicate, clean and tends to feature smooth clean woods (cedar) accented with soft spices and moss (cardamom, oakmoss).
Animalic Musks tend to emulate the original, potent scent of the natural musk extract and feature added notes of civit, ambergris, castoreum, patchouli, etc to create the same erotic effect.
Why not order up a mini sampler of musk based samples to explore so that you can understand the differences a bit more?
Ava Luxe has a good range of simple musk blends. A possible 'Musk Sampler' could include:
Cashmere Musk - Clean, with soft sweet floral notes
Egyptian Musk - A clean and creamy soft skin musk with universal appeal.
Nude Musk - A clean skin musk with notes of sandalwood, bergamot, light musk, and vanilla. Light and slightly powdery.
Tunisian Musk - A dark warm floral musk with resinous incense overtones.
Oriental Musk - A slightly sweet and powdery exotic musk with hints of jasmine and tonka.
Incense Musk - A deep rich and thickly textured musk with incense, resin notes and spice overtones.
Dancing Queen - This is a classic '80s musk, rich and distinctive with a wonderful powdery feeling and hints of soft florals and woods.
Kama / Kama Xtreme - Kama is a blend of musks with a high content of erotic-animalic notes. A touch of rose absolute adds softness.
Rasa / Rasa Xtreme - Rasa is a blend of musks with a high content of erotic-animalic notes. A provocative blend of musks infused with spicy red rose. This is good as it contains a blend of at least four typical musks: Indian Musk, Kenya Musk, Skin Musk, Egyptian Musk.
Nemat International also have a great selection / variety of musks worth exploring. These tend to be richer and rawer, less 'processed' in feel.
In the US these can be found in local Whole Food stores in regular sizes. It is also worth while contacting the company direct.
I do hope this helps somewhat.