What is the difference in Voice Commands and Voice Search? Are they both by Google?
Voice Search is the name of the voice interaction app created by Google. It allows you to search your phone and the web using your voice.
Voice Actions is a specific feature of the Voice Search app that allows you to perform actions on your phone using your voice (such as calling someone, launching your music player, getting directions, etc). Voice Search supports a variety of locales but the Voice Actions component is only available for a subset of those (originally US English only, though I believe it has since expanded).
If you have a separate app named "Voice Commands" then it is most likely developed by a third-party. I know some Verizon phones, for instance, ship with an app named "Voice Commands" and bottom of the app displays