How do you display your movies to your Smart TV if it is not an Apple Tv? I have Chromecast but I cannot figure out how to cast the movies to my TV.

You cannot "cast" iTunes movies to a Chromecast. you can cast things like the Youtube App and other supported apps, but not movies from iTunes.

See here: https://en.wikipedia.org/wiki/List_of_apps_with_Google_Cast_support

To play movies purchased on iTunes on a TV you have the following options:

1. An Apple TV (you can stream direclty on it, or Airplay from the TV App on an iOS device)
2. TV with the Apple TV app or one that supports Airplay 2,
3. You can connect the iPhone directly to a TV using an HDMI cable with a Lightning Digital AV Adapter - Lightning to HDMI - Apple

See here: Apple TV app - Devices - Apple

and here: How to AirPlay video and mirror your device's screen - Apple Support

That has nothing to do with Apple TV. That’s a Google app. Maybe this will help.

https://support.google.com/chromecast/answer/3228332?hl=en&ref_topic=4602553