I think the words seem and look are synonyms here.
In many cases it can be but doesn't have to be.
son to father: You seem upset, dad.( he really doesn't know for sure, dad just appears upset)
dad: Oh no, I am fine. I am just thinking about something and it's been on my mind for a while.
son: you look angry dad! ( he knows he is in trouble, and YES, he can say you seem to be upset as well!)
dad: you bet I am angry. I haven't seen you do any chores around the house in the longest time! You expect your mother to do everything for you.
somehow seem adds a little bit of subtlety to the statement, I think.
"seem", technically, is used when you go by the appearance of something.
The patient seemed to be in good health, however the blood test has revealed problems with his liver.