When are two database objects equal? The answer is: it depends! It depends on what you want to compare those objects on - for example: is "Equal" equal to "equal"? The comparison options allow you to have complete control over the comparison engine which considers those options before deciding to mark a pair of objects as equal or different.
So, when two objects are found to be different by the comparison engine while you believe they should be equal, or they are found to be equal while you believe they should be different don't panic - investigate the differences and carefully review the comparison options - more likely than not one of those options holds the answer to your surprise.
The comparison options tab provides a description and important remarks for each option while also allowing you to turn those options ON or OFF. To view the description and remarks for a given option simply move the mouse over that option as shown on the image below.