[From "Overview"]

Chrysotile and Asbestos Amphiboles: Two Different Fibre Types
Asbestos
"Asbestos" is not a mineral in itself. It is a collective term given to a group of minerals whose crystals occur in fibrous forms. The term "asbestos" was adopted for commercial identification

The six minerals commonly referred to as asbestos come from two distinct groups of minerals. One group is known as serpentines (chrysotile, white asbestos); while the other group is the amphiboles[…]While both are silicate minerals, the two groups are chemically and mineralogically distinct
Chrysotile
Chrysotile is a sheet silicate which is formed as a very thin rolled sheet[…]
Chrysotile has been known for over 2000 years, being used initially for cremation cloths, oil lamp wicks and other textiles[…]
Amphiboles
This is in contrast to the amphibole asbestos fibers which are formed as solid rods/fibers. The structure of an amphibole is a double chain of silicate tetrahedral which makes it very strong and durable[…]
In contrast with amphiboles, chrysotile does not persist in the lungs after inhalation; it is quickly eliminated by the body. A prolonged exposure to high concentrations of chrysotile fibres is required for a clinical manifestation of pulmonary damage to appear[…]
Chrysotile: controlled use = safety
Chrysotile is a less dusty material and is more easily eliminated from the human body than amphiboles. The manufacture and use of modern products are safe as demonstrated by studies of workers exposed to much higher dust levels than in today's controlled factories which show no excess lung cancer or mesothelioma (cancer of the pleura)[…]
Chrysotile and its non-friable products[…]can be used safely[…]This is the position taken by the governments of Canada and Québec, regarding not only chrysotile asbestos, but all minerals and metals