Charley and Bernard act as a foil for Willy and Biff. The first pair is a father and son dyad whose relationship is fortified by the daily nuisances of life that bring people together: Working through issues, supporting one another, accepting mistakes, and bringing each other up when the going gets tough. Charley does not demand anything from his son, Bernard. He has no expectations for him except that hoping that his son is happy and does the best that he can to succeed in school.
Like Willy, Charley is a hardworking man. His son helps Biff with math and also tells Biff over and over that he (Biff) should get serious about school, and that college is right around the corner.
In a similar fashion, Charley helps Willy by lending him a couple of dollars when the check comes home low, and encourages him to get a better job.
Ironically, Charley and Bernard are both treated by Willy and Biff as unpopular and boring, even though they have been nothing but kind to the Lomans. Keep in mind that these two families are neighbors and friends, regardless. They also share together, support one another and even root for each other, as well. Their differences have never put a damper on their relationship.
Willy and Biff
The second pair, Willy and Biff, are a symptom of Willy's view of life and how it should be lived: shortcuts, loopholes, and shallow competition.
Willy is a traveling salesman who wants to get rich quick. He claims to be a great salesman, but in reality he has not achieved very much. His idea of succeeding is that of being "well-liked" and popular. Likewise, he encourages his son to continue to focus on football, not school, since a football scholarship will get him to college, and perhaps even into professional sports.
Biff, who adores his father and follows his example, has blindly accepted Willy's vision of who Biff really is, and what he will become. Yet, Biff will discover later on that he has lived a fantasy his entire life. This fantasy, propelled by Willy, places Biff at a really high place where Biff is great, and is meant to achieve amazing things. Far from wishful thinking, these constructs are very real to Willy Loman. So real, indeed, that he goes through his entire life believing all of this to be true, and so does Biff, for a while.
All this being said, here is a shortcut of differences between the two relationships"
1. Charley raised Bernard without expecting anything in particular from his son, and both (father and son) are entirely down to earth. Willy raised his sons calling them "Adonises", allowing them to be bullies, and encouraging Biff to feel superior to the rest.
2. Charley was supportive of Bernard's academic achievements. Willy was obsessed with Biff's prowess in football, by his son's good looks, and by his slick and cheeky attitude towards teachers.
3. Charley did not intervene in trying to make his son look or appear to look in a specific way. Willy was an enabler since very early in Biff's life. Anything from bullying, to theft, was always forgiven with a good excuse to justify Biff.
The result of each of the parenting skills says a lot of how influential parents are in the lives of their kids.
Bernard went on to college, finished school, then went to law school and became a litigating attorney. When Willy sees him for the last time, Bernard is on his way to argue a case in the Supreme Court. Willy is shocked at everything. How was Bernard able to figure out his life, when neither Willy, nor Biff, nor Happy have been able to do that very thing?
Bernard explains to Willy that the summer when Biff failed math, he (Biff)had gone to visit Willy on the road.
Rather than finding succor and support, Biff finds a woman in his father's hotel room. This is to Biff more than enough evidence that uncovers his father as a liar and a cheat. What else could Willy have lied about? About Biff's greatness? About Biff's sure-to-be successful life? That seems to be exactly what went through Biff's mind. After returning to New York, Biff no longer cared for anything or anyone. His life, as he knew it, was over.
One last thing to consider is the cohesive factor. Willy and Biff are in a consistent quarrel. Biff always ends up gravitating toward Willy, not because he likes his father that much, but because his image and self-awareness depended so much on what Willy made of it, that Biff is essentially crippled by psychological co-dependence. He goes and returns. Toward the end, however, he will want to leave for good.
Bernard, on the other hand, is found at his father's workplace before going to the Supreme Court to litigate a case. This shows that, in contrast to the Lomans, Charley and Bernard remain well-bonded, the way it should be.
In not so many words, while both parents have done the best they can to help their children, the personal issues of Willy superseded any want to make his kids become successful the right way. Charley had no views, nor dreams, nor expectations. As a result, he allowed his child to grow and discover who he is, with much better results than those of the controlling Willy.