Are the "upper hand" and the "white hand" the same thing? And what is the meaning of the phrase "you have the white hand"?

The preponderant interpretation of the Hadith is that the upper hand is the one that spends, and the lower hand is the one that begs. This is supported by what is stated in Sahih Muslim: "The upper hand is better than the lower hand, and the upper hand is the one that spends, and the lower hand is the one that begs." The term "white hand" refers to a favor and kindness free from reproach or harm. So, your colleague's statement, "You have a white hand over him," means that you have done him a favor.