To Naruto, they were family. He knew that Iruka was the father, Kakashi the eccentric uncle, Jiraiya the perverted and knowing grandfather. But what were Sasuke and Sakura? Siblings? Cousins? Husband and wife? He didn't know, but they were still an important part of his family.
To Sasuke, they couldn't be family. It was either the pain from remembering his original and replacing them, or the thought that he would loose Sakura and Naruto like the first. But they were still important to him; they were his teammates, they helped him learn, even if he had to leave them.
To Sakura, they were her partners, friends, crushes, all rolled into one. She wanted to be the loving family of Naruto that he could play around with, the loyal teammate of Sasuke that he could rely on to always watch his back. They were everything to her, and she wanted to be everything for them.