I don't think that syntax is correct.
apt-get update - installs the updated lists of what's available
apt-get upgrade installs updates which debian, for reasons of it's own, refer to as 'upgrades'
Presuming the 2 machines are in synch presently, I would use the online machine, run sudo apt-get update, and then when you run 'sudo apt-get upgrade' it spits out a line or many lines of what's going to be upgraded. RETAIN THAT INFORMATION!
Now there's some option (maybe in dpkg) that allows you to download the packages. You can get them on a usb key, carry them over and manually install/upgrade them. There's also documents on creating your own repo