There are different terms associated with a group of people fighting. Sometimes they are called militia and insurgency. However, they are used for different sizes of the groups fighting and if they are supported by the government. Also, the length of time the fighting has been going on is also taken into account.
A militia is usually a group of people fighting usually opposed to what is happening in the government of their country. They may even be fighting against their own country because of the laws and corruption that is happening in their federal government. An insurgency is similar to the militia but they are not deemed as being belligerent. They are merely rebelling against the leaders of the country.