There are several different types of wood used in Cricket Bats, the two major types are Kashmir Willow and English Willow. Kashmir Willow is native to India and Pakistan, and grows in the wild. On the other hand English Willow (Salix Caerulea or Alba Var), used in the manufacture of cricket bats, is grown in plantations specifically for cricket bats. It may sound stupid, but English Willow is grown in England - Willow grown outside English is NOT English Willow.
How to tell the difference between English & Kashmir Willow
On inspection English Willow will be much whiter than Kashmir Willow, and will have more well defined or obvious grains. Kashmir willow also tends to have a red/brown colour to it and its grains will tend not to be particularly straight or uniform, due to the growing conditions.
Below are examples of both English and Kashmir Willow, the Kashmir Willow bat is poly coated.

English Willow

Kashmir Willow
Performance of English and Kashmir Willow
English Willow is the best material to use in a Cricket Bat. It is much softer than Kashmir Willow, and thus has much better performance. Additionally Kashmir Willow is dryer and more brittle than English Willow.