Eric,
The code that Tealium injects onto the site is different because it contains a lot of Tealium functionality built in. The code you pasted above is the Tealium template for the Google Adwords Tag.
Tealium not only has to include what Google provides but it also has to provide functionality for Mappings, E-Commerce Extension support, and support for any other extension you add via Tealium.
This is why the code base doesn't look the same.
However, if you instead look at the server call that is made to Google Adwords then you should be able to see that the server calls created are the same. This is assuming the tag has been configured properly.
Cheers!