I would say that the theme of happiness and belonging are one in the same. One of the reasons why the protagonist wanted to pursue a life of happiness as defined as working hard to make a lot of money was for the sake of another. In other words, due to relationships, namely his son, he wanted to work hard. We can even say that he wanted a sense of belonging and wanted his son to have a sense of belonging. So, in this way, the pursuit of happiness and sense of belonging are related. Also it is this relational aspect that make the work deep and not superficial.
One of the critical themes of the film is how individuals perceive those who are on the "outside" of our social order. Chris Gardner starts out the story belonging to the world of wealth, privilege, and respect. Through financial challenges, he is relegated to the outside. His desire to belong to a world of stock brokerage is sustained through his belief in his dreams and the commitment he has to his son. He is animated by his desire to belong, and his desire to link his dreams to success that comes with belonging. The film shows that if one seeks to belong to something and this is embedded in their dreams, then it can be accomplished so long as individuals show their commitment and are not afraid to take the opportunities presented. In this light, dreams and belonging go together quite well.
Are you referring to the movie? If that is the case, then the sense of belonging relates to the audience members who can identify with the hardships Will Smith's character endures. Think of all the choices and disappointments his character experienced. The belonging can also relate to his wanting to be a member of that society on Wall Street. He wanted to be a part of a society that seemed to be "happy." He wanted to belong to a society of respected men and women who were not constantly worried about money. This is a theme that is particularly relevant to society today.