DIRECTV and Dish Network are different companies. DIRECTV is owned by Hughes, Dish Network is owned by Echostar. It's kind of like the difference between Charter Digital Cable and Comcast Digital Cable...similar service, feature-wise, each has their pros and cons.
As far as Tivo goes, that is a service on its own. DIRECTV and a Tivo/DIRECTV integrated receiver. Dish Network's Digital Video Recorder doesn't have a monthly fee as stated above, but I'm not sure how it compares to the quality of Tivo. I would definitely recommend checking out the interfaces on both systems if you are comparing DIRECTV to Dish Network.
Here's an interesting site for more info:
http://www.dish-network-vs-direct-tv...-direct-tv.htm
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