The Greasers in the book are the poor kids from the "wrong side of the tracks" so they don't really know much about their rich enemies, the Socs.
The Greasers (specifically Ponyboy and Johnny and Two-bit) find out more about the Socs when they go to the movies and meet Cherry Valance and her friend Marcia. They hang out with the two girls for a while and find out that they are not really all that different than the Greasers -- just that the Socs like the Beatles more than Elvis.
They do find, however, that the Socs are less emotional than the Greasers and that they (at least Cherry) feel like their lives are less meaningful.
The other way Ponyboy, at least, finds out more about the Socs is when Randy, the friend of Bob (who Johnny killed) talks to him a couple times -- once before the rumble, and once at Ponyboy's house. When he does that, he finds out that Randy has some of the same feelings he does about fighting and that Randy feels like he's let his dad down.
The Greasers in Hinton's book "The Outsiders are a group of boys who live in a lower income neighborhood. The Socs are their rival and enemies. They live in two different worlds. The Socs have nice cars, nice clothing, and tailored haircuts. Despite these things they are in conflict and seek conflcit with the Greasers. They really have only stereotyped one another and know little about each person other than seeing them as a collective group.
The dynamics begin to change when Pony Boy, Johnny, and Dallas are at the drive-in movie. Pony Boy meets Cherry. She is the girlfriend of the Soc called Bob. In ignorance to the idea that Socs have problems, Pony Boy tells Cherry that Socs don't feel deeply like the Greasers. He thinks of them as being more emotionless. Cherry counters his ideas by explaining to him that Socs have problems too.
Later in the book, after Johnny and Pony have saved the children form the fire, one of the Socs goes to talk with Ponty Boy. He explains to him that Bob had problems and that he had cared about Bob as his friend. However, he does understand that the whole incident was their fault and that he would testify. Pony Boy and the Greasers begin to see that they have some things in common with the Socs. Two of them are willing to stand up on behalf of Pony Boy.