At the moment, you can't separate those two permissions issues. However, feel free to put in a feature request to support@buildwithcraft.com or the Google+ community.
As a workaround, here's what I have done... You can automatically assign a user to a group upon registration.
Change the permissions of your main user group to lock them out of all "Users" management permissions. Add a business logic plugin to your site (if you don't have one already).
Put this into the init method of your plugin's main class...
public function init() {
parent::init();
craft()->on('users.saveUser', function(Event $event) {
$targetGroupId = 1;
// If new user
if ($event->params['isNewUser']) {
// If "groups" is in POST
if (isset($_POST['groups'])) {
// If not an array, it's an empty string
if (!is_array($_POST['groups'])) {
// Set it to an array with the user group ID
$_POST['groups'] = array($targetGroupId);
} else {
// Merge in the user group ID with any existing ones.
$_POST['groups'] = array_merge($_POST['groups'], array($targetGroupId));
}
}
}
});
}