Can't seem to find the difference between these. D6 is what I need to know, but would love to know how those looks into 7 and even 8.
The root URL of the host, excluding the path.
The base URL of the drupal installation.
again, e.g. http://localhost
The only situation I can think of where these would be different is if your Drupal installation is in a sub-folder of the web root. In that case
$base_url would also contain the sub-folder in the path, e.g. http://localhost/drupal
The descriptions in the documentation are exactly the same for both across versions 6, 7 and 8.