Advanced TV HD Receiver versus Digital Mini Box?

Can anyone explain to me the difference between the function of  a COX Advanced TV HD Receiver and a COX Digital Mini Box?

We downgraded to TV Economy but still connect to cable TV service via a COX Advanced TV HD Receiver. The charge for this device is $8.50 each month. The new COX Digital Mini Box that Cox suggests everyone to get sounds like it performs the same function, however, it sounds as though it's free for one year and afterwards the monthly fee would be lower than we're presently paying the Advanced TV HD Receiver.

If this is true, we'd just as soon switch to the Digital Mini Box. Can anyone confirm that the Mini box does the same thing as the Advanced TV HD Receiver? Thanks.