Chromecast, as I understand it, is primarily a device for streaming content from a phone or tablet across to your TV. (i.e. you need to have BOTH a Chromecast AND another device, capable of receiving streamed TV signals, to get it to work).
I've not encountered the term 'Android TV box' (and Google isn't particularly helpful, so I'll pass on that one.
What you might see in the shops are Tivo boxes, which are rather similar to Now TV boxes. That's because Now TV boxes are actually TIvo boxes that have been specially configured to Sky's requirement (because it's Sky which markets them).
A Now TV box (on its own) does indeed cost just £9.99 (inc p&p). However (if you buy online) you can also get the box complete with one of the following options for £19.99:
a) a 3 month 'Entertainment' pass ; or
b) a 2 month 'Movies' pass ; or
c) 2 x 1-day passes for access to all 7 Sky Sports channels.
It's those 'packages' which are on sale in major supermarkets. (If you're interested, be sure to pick up the correct box, as all three are usually close together on the shelves). I paid £16 in Asda but Tesco had them for £20 with £2.50 in Clubcard Reward points (in addition to the normal 20p) given with your purchase.
Once you've got your box you have to register online for an account, so you can activate your package. You do need to provide your debit card details but unlike, say, Sky or cable services, there's no commitment to a subscription. You simply tell them if you don't want to pay £6.99 per month (for the Entertainment pass) after the three months are up. Your box will still work with 'catch up' services (such as BBC iPlayer ITV Player, 4oD and Demand 5) and free apps (such as the one that let's you watch Youtube videos on your TV or access internet radio stations from across the world).
I'm extremely pleased with mine.
http://www.nowtv.com/box