What distinguishes George and Lennie from everybody else is that their dream involves community and fellowship rather than being an isolated dream of future and success. This is identified in the very first chapter when Lennie asks George once more to talk about their dream and what it will look like. Note how George responds:
Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don’t belong no place... With us it ain’t like that. We got a future. We got somebody to talk to that gives a damn about us. We don’t have to sit in no bar room blowin’ in our jack jus’ because we got no place else to go. If them other guys gets in jail they can rot for all anybody gives a damn. But not us.
Their dream makes them different as it represents the antithesis of the spirit of loneliness and the sense of lack of purpose that broods over the entire novel. The dream that Lennie and George have is therefore different from the dreams of other characters because it involves them facing the future together and having somebody who "gives a damn" about them.