the smtp server to use with outlook is not necessarily the same as the one to use when sending mail through php script.
there is a difference in sending mail through a php script and sending mail though an email program.
In a php script, you do not have the option of passing a username and password to the smtp server. your host should have an smtp server set up that will allow the php script to relay the email, it will not be the same mail server you use when configuring outlook.
If you are using the correct smtp server, then you need to look in the error logs to determine why the email is not being relayed.
The script will pass the email to the email server. The email server then relays the email to the recipient. If that relay is failing, you need to look into the error logs to see why.