What's the difference between 差異 and 差別? Do both of them mean "difference?" Not sure if they are the same part of speech or if they are interchangeable.
Both 差異 and 差別 mean "difference"


差異 = (physical) difference 
差別 = (physical or metaphorical) difference  


Example:

这两张牌全无差異/这两张牌全无差別  (these two cards have no difference)

the two cards are physically the same

对我而言，有机食品和普通食品之间並无差别  (to me, there's no difference between organic foods and common foods)

the two products have the same food value to me


  you cannot replace 差别 with 差異 here because the difference between them is not physical but of value in your opinion.


One more example for 差别 used to describe metaphorical difference: 

输给彼得或输给保罗是一样的，没有什么差别 (lose to Peter or lose to Paul are the same, there's no difference)

the main point is you lose


  Again, you cannot use 差異 instead of 差别 here because the focus is not on the physical difference between 'lose to Peter' and 'lose to Paul' . The focus is on the win or lose result)