I know this can be confusing at first, but subfolders/directories can have completely different index.php files. For example the 2nd file you mentioned /htdocs/lakecontractingwordpress/wp-admin/index.php is actually the main file of the admin (dashboard) area of your website. It's not the same file as /htdocs/lakecontractingwordpress/index.php
Both of these files are Wordpress core files and it's never a good idea to edit these directly, because any time you update to a newer version of Wordpress your changes will be lost.
If you just want to change your navigation menu links, you can safely do this via the Wordpress dashboard by going to Appearance->Menus.
But if you want to change the header logo link it's more complex. The reason it's pointing to http://lakecontractingftpco.powweb.com/lakecontractingwordpress/ and not http://www.lakecontracting.com has to do with how Wordpress has been installed and configured on your server. If you want to change this, tech support at your hosting provider should be able to help.