I can send email from outside but not using phpmailer (error 111)

I can send email via my webserver from my computer (using Thunderbird), but not from my website using 'phpmailer'. Oddly enough, when I run 'telnet mail.myserver.com 25' on the server, it says 'connection refused', the same error message I'm getting with phpmailer (error 111 – "Connection refused"). However, emails are sent fine through Thunderbird (which is set up to port 25 also, only to use encrypted passwords), I can also connect with telnet just fine from my computer to the mail server.
Any idea what may be the reason for this strange problem? I'm using the latest phpmailer version, and the CentOS7 server is running php 5.6.18.

Output of netstat -an | grep 25:

tcp        0      0 0.0.0.0:25              0.0.0.0:*               LISTEN
tcp6       0      0 :::25                   :::*                    LISTEN

Phpmailer config:

require_once("./stuff/phpmailer/PHPMailerAutoload.php");
$mail = new PHPMailer();
$mail->IsSMTP();
$mail->Host = $SMTPHOST;
$mail->SMTPAuth = true;                 
$mail->Port = 25;
$mail->SMTPDebug = 2;
$mail->Username = $SMTPUSER;    
$mail->setFrom($email,$name);
$mail->AddAddress($AdminMail);
$mail->Subject = "Here is the email";
$mail->Body = "I am an email";
if(!$mail->send()){..}

By the way, PHP's mail() method works also, only SMTP seems to cause the problem. So when I change $mail->IsSMTP() to $mail->IsMail(), it works.