What is the difference and the similarity between Squeaky and Gretchen?
Both Squeaky and Gretchen are similar in the sense that both are competitive girls who are focused on winning the race.
In the beginning, both are wary of each other. Squeaky dislikes Gretchen because a former friend has now taken up with the new girl. Mary Louise used to be Squeaky's friend, but she's now taken to gossiping about Squeaky behind her back. From the text, we can see that none of what Mary Louise says to Gretchen about Squeaky is complimentary. Gretchen's other side-kick isn't much better: Rosie is loud and often insensitive in her remarks about Raymond, Squeaky's mentally-handicapped brother.
However, one thing different between Gretchen and Squeaky is the way both girls relate to Raymond. Squeaky, being Raymond's sister, is very aware of her brother's presence in the background, whether before, during, or after the race. Even when she wins, Squeaky's thoughts center on Raymond; she thinks about coaching him and helping him to win medals. After all, she's won more than her fair share, but Raymond has none to his name. To Gretchen, however, Raymond is just another girl's brother. He doesn't figure much into her thoughts. The only thing she knows about Raymond is that Squeaky is extremely protective of him; she understands that Squeaky will never tolerate her treating Raymond badly (intentionally or unintentionally), so she keeps her distance from the boy.
So, Squeaky and Gretchen are similar in the way they approach winning but dissimilar in the way they relate to Raymond.