How does an opportunity cost differ from a trade-off?

An opportunity cost is the loss of possible gain from other alternatives when one is chosen, a trade-off is the course of action given up to perform the preferred plan of action (or campaign or attack).

the conditions that made the byzantine empire vulnerable to attacks by the muslin turks were the sack of constantinople by western crusaders, the conquests of the sultanate of rum, presence of rival kingdoms and finally the set up of fiefdoms at the empire which were owned by the ghazis (turkish warriors).