do people see me online on fb even if I'm not even there (but signed in ) ?

[nadia]

I recently discovered that if I sign in to facebook people automatically see me online on fb chat even if I have it turned off !!
Now I always knew that I can appear offline to certain people but then I never really tried to do so because most of the time I already have facebook chat turned off beacause I don't like chatting . I'm not asking you how can I be invisible because I now know that there is a difference between turning off chat and turning off chat for specific people , my question is , what's the point of going offline if people can still see that you're using facebook ? is there a difference on how I appear in their list ?also if I left but I forgot to sign out and I come back after hours , during that long period do people still see me online or is there an indicator that I'm signed in but I'm not clicking on anything ?
@sasha thanks but what if i never close the page and leave my laptop for hours