Final answer:
Both Crusades and Jihad involve religiously motivated warfare, but the principles of 'just war' complicate them due to variations in their historical application and evolving interpretations within each religion.
Step-by-step explanation:
The commonalities between the Christian ideas of crusade and the Islamic ideas of jihad include both being forms of religiously motivated warfare. However, defining what constitutes a 'just war' complicates these concepts. While both crusade and jihad were to be called by proper authorities within their respective faiths, the application in history has been varied, and not always aligned with the principle of 'just war' as defense and with proper declaration from leaders. Moreover, the conceptions of just war evolved over time, influenced by interactions and conflicts between Christian and Muslim territories.