Is Apache Tomcat built on Apache Web Server platform?

Recently our Software Analytic provider (NETTRACKER) sent us a plugin in order to be able to capture visitors in a better way. This plugin is for Apache 1.x and Apache 2.x. They said and I quote

that since Apache Tomcat is built on Apache HTTP server the configuration of the plugin should be the same.

I have looked for a httpd.conf in our tomcat deployment but we cannot find one, the only configuration that is similar to that one is the server.xml under the /conf directory.

If someone has better information regarding these two incredible products (Apache HTTP server and Apache Tomcat) I will greatly appreciate to draw the differences.

EDIT:
In case you are curious we know that Apache Web Server and Tomcat can work together using the mod_jk option and other proxys. But this will be too complex for our deployment.

Which rewrite rule am I missing(ISAPI on IIS)?

I have the following rules:

RewriteEngine on
RewriteCond %{HTTP_HOST} ^www\.example\.com$
RewriteRule ^blog/?$ http://blog.example.com/ [P]
RewriteRule ^(blog/.*)$ http://blog.example.com/$1 [p]

RewriteCond %{HTTP_HOST} ^example.com$ 
RewriteRule ^(.*)?$ http://www.example.com/$1 [L,R=301]

What I’m trying to achieve, and it works up to 90% of my expectations, is that any hits to http://www.example.com/blog proxies over to http://blog.example.com. The issue I have here is that if I visit http://blog.example.com/some/dir/foo.php it works fine. However, if I go to http://www.example.com/blog/some/dir/foo.php, it does NOT work.

What rule am I missing?