As far as i know, there have 5 different styles cap according to the difference of material.
Felt hat: It is made of 100% wool. This kind of hat is very popular in the formal occasion.
The women and old men like to wear it in winter.
It is a traditional hat in western countries. But no people wear this kind of hat in China.
Leather hat: leather hat only can be worn in winter season. This style of cap will be ordered by police or army at most condition.
Knit cap: knit cap is also suitable to wear in winter. This style winter cap now is very popular ,especially for the youth boy and girl.
Straw hat: straw hat is worn in the summer. In china, only a few places can produce this style hat.
Baseball cap: Baseball caps is made of fabric. It can be worn in the spring ,fall,winter. This style cap has big demand.