Why won’t wp_mail() let me set the From: header when plain old PHP mail() will?

When I use wp_mail( $to, $subject, $message, $headers ) (with values in place, of course), the email gets sent with a from name and email that isn’t set anywhere I can find (not even in PHP or Apache settings). However, using mail( $to, $subject, $message, $headers ) instead works just fine. What could be happening with wp_mail() to cause this?