You are looking to implement NTLM Authentication in the PHP application, see my prior answer on this:
http://stackoverflow.com/questions/635171/can-a-php-intranet-share-windows-logins/635230#635230
You are looking to implement NTLM Authentication in the PHP application, see my prior answer on this:
http://stackoverflow.com/questions/635171/can-a-php-intranet-share-windows-logins/635230#635230
If your other web application uses Windows Integrated Authentication (NTLM or Kerberos authentication or even basic authentication) then it can act the same way. Depending on the browser, it can automatically remember and log into sites using one of these methods. Each browser may do it differently, though. IE has settings for automatically logging in based on the zone (Internet, Local intranet, trusted sites).
You would not necessarily need to have the have your other application use the same user store (AD/LDAP), but it would likely make sense.