TVE is shorthand for TV Everywhere. It is a technology that TV networks use to stream live TV. An example would be cnn.com. When you go to cnn.com, there is a live TV link, which allows you to log in with your TV Provider (Cox, Youtube TV, Spectrum, etc). Once you have verified that you are a subscriber then you can watch live TV from the cnn website.
Channels is a DVR application that will work with TVE websites.
My assumption was the 'ESG' was just a typo for EPG.