I have a site, when I log in with the same user with two browsers, the session_id() tells me the same value. Isnt it wrong? How to distinguish the two users?
UPDATE/EDIT: Google Chrome seems to have a SERIOUS issue with exactly what you wrote, see this Chrome is creating duplicate sessions with the same id and http://code.google.com/p/webug/issues/detail?id=12 for more info.
My older answer:
If you are REALLY using two different browsers, then you are probably
Typical PHP sessions are created as files on the server filesystem, so a "new browser" does not know about this session and the browser has no info about you that it could send to the server.
If you want a REAL answer, show some code, dude.