There are two main types of mane and tail combs- plastic and metal. A comb is often used on the mane to remove tangles, but care should be taken to minimize pulling the hairs out of the mane. Snarls or large tangles should be combed through and never cut out of the mane or tail.
Tails should be encouraged to grow long and full, therefore combs should not be used. A preferred method is to spray tail with some type of detangler solution and then use the stiff brush, or gently separate the tangles with your fingers. Conditioners can also be used on the tail to keep it free of tangles.
For more information about grooming, check out How to Groom a Horse and Grooming for Success.