Though their duties and nature changed over time, Christian orders such as Knights Templars and others were created by Western European Christians to protect the lives and interests of christians and christian pilgrims in Holy Lands. Since holy lands were essentially foreign lands for western Europeans, these orders were created as institutions to protect their interest in distant lands as response time from europe will be too long if there is urgent need. Saracens in the other hand were native to the region had no need for such orders and institutions and therefore there were no crusade specific institutions on Muslim side.That being said there have always been armed groups throughout Islamic history pursuing one goal or another and all these groups comes under the umbrella term of "Mujahideen". Similarly infamous Nizari Ismaili order of Assassins was active during the period of crusades and Syrian branch of the order sided with Saracens and fought against crusaders in 2nd and 3rd crusade.