Simple Answer
This is the difference between the extremely pious religious person and the religious person who tries to enact his religion through law. (Compare, for example, the Westboro Baptist Church, whose members are extremely pious, but do not try to change national laws, and the Evangelical Conservatives who actually try to overturn Roe v. Wade in the US.) A person can be both an "Islamic Fundamentalist" and an Islamist, but these refer to two different aspects of this person.
Explanation
It is important to note, first that Islam is a religion, but Islamism is something else. It is a political ideology whose goal is to bring the religious tenets of Islam into the daily functioning of a government and its laws. Islamism is a modern movement whose roots began contemporaneously with the rise of Salafism in the late 1800s and early 1900s in Egypt. Islamism is not by nature violent or expansive. Many Islamist movements have concrete nationalistic goals such as the Islamists in power in Turkey.
Islamic Fundamentalism (Usuliya or Salafism) is a religious position about how a person should live their life. It concerns personal implementation of the Shari'a law. It is not necessarily violent, but most Fundamentalists (Usuliyin or Salafists) cannot separate their personal desire to live a puritanical life from their demand that others join them and set up laws requiring a country or the world to adhere to their views.
Main Difference
Usuliyin or Salafists can be Islamists and vice versa, but Usuliya or Salafism is how a person decides to believe in Islam. Islamism is the political implementation of Islamic Laws. Not all Islamists are Usuliyin or Salafists (like the Tunisian and Turkish Islamist Parties), but some (like An-Nur in Egypt) are.