Is it normal to feel like two different people?

I often feel like I am two different people, two different strangers to be exact. I mean, it just seems like I'm one person at school with my friends and one person at home with my family/alone. However, none of this people feel like they are me. At school, I am usually quite smiley and I laugh a lot and joke around. However, at home, I am cold, distant and emotionless. You will never catch me smiling or laughing at home (unless I'm alone.) At home, I also think really depressing thoughts unlike at school. It feels as if I think of nothing at school. Is this normal? Do I have some sort of personality disorder?