The term 'Islamist'

Having just read an article about someone who was "speaking out against Islam and Islamism," I realise that I have heard the terms 'Islamist' and 'Islamism' quite a bit recently.

This is causing me a bit of confusion... not from a religious standpoint, but from a grammatical view.

I'm assuming that an 'Islamist' is a person who follows Islam. And I'm also assuming that 'Islamism' is the term given to the set of beliefs that 'Islamists' follow. Please, if I am wrong in these assumptions, can somebody correct me!!

Because...

I thought that a person who follows Islam is called a Muslim. And I also thought that the term given to the set of beliefs that Muslims follow is just Islam. In other words:
Islamist = Muslim
Islamism = Islam

In summary, why on earth are there two extra words being used when the English language already has the words to describe those things?!?!


EDIT:
I have recently found that the term 'Islamist' effectively refers to Muslim extremist and 'Islamism' to the set of beliefs of such extremism. This is to differentiate between those who use Islam to practise terrorism (or use terrorism to practise Islam?) and the amicable Muslims who simply practise their faith in a non-destructive way... according to my current understanding!