Hi there,
you’re talking about AD -> do you mean Microsoft Active Directory? If yes it has nothing todo with Samba!
It would be helpful if you would post your entire LDAP config here.
Have a look here for a working MS AD LDAP configuration.
The bind_dn should be every time in the form of your 1st or 2nd example. MS AD is not case sensitive so both will work. For other directories this can be different and I guess that for this configuration active-directory should be false all the time.
Good luck!