Windows 8 has certain guidelines for the Modern Apps - one such being the absence of the Title bar & the minimize/maximize/close buttons.
Google Chrome looks different when opened from Start Screen than when opened from the Desktop if it is set as the default browser.
Windows 8 sets a default program for each service - For instance, one for the browser, one for opening PDF files, one for opening photos and one for watching videos. If you have set IE as your default browser, you would see Google Chrome opening in the same familiar way, irrespective of how you opened it (and you wouldn't see the black bar). However if you set Google Chrome as the default browser, opening from the Start Screen leads to Windows 8 recognizing it as a Modern UI App (since its the "default" program for browsing) and requires it to be opened in the Modern-UI mode - striping off its Title bar & making it look different (and hence the black bar). Opening it from Desktop poses no such restrictions and hence you see the familiar Google Chrome UI.
About dragging it - you can drag it down to close the browser and if your screen resolution supports it, you can drag it left or right to pan it on the side.