Both Chromebook and Chromebox are devices that run Chrome OS and are cheap when compared to laptops and desktops. Chromebook is a laptop alternative and Chromebox is a desktop replacement. Let us know in detail about these two devices.
First Chromebooks were introduced by Samsung and Acer in 2011 and later every company started producing these ultraportable and simple to use devices. They are designed in a way such that they can be used only when connected to the internet. However, there are some apps that run offline like Google Calendar, Google Keep, and Google Drive etc.
Chrome box is a desktop replacement which looks similar to a set top box and even it rely on internet connection to offer complete functionality. These Chromeboxes are costlier than Chromebooks and only four brands (Samsung, Google, HP, Asus) are offering them at present.
You'll need a separate monitor for Chromebox and you can use your own peripherals like keyboard, mouse, speakers etc in addition. Google's Chromebox is a mini PC that come bundled with a webcam, remote control, speakers and microphone and Samsung offers wireless devices for Chromeboxes.
These two devices Chromebook and Chromebox are just replacements and have compromised functions. They are available for a cheaper price and can give you complete functionality only when connected to internet. Hope you got an idea on them.