As far as you're concerned, Linux *is* Unix. As to what each of them really is, that debate could go on for ages.
You might find this helpful:
http://bhami.com/rosetta.html
It shows how to do various functions on various flavors of Unix. For example, to determine your IP address.
As far as connecting to Unix boxes together, the simplest manner is NFS, or Network File System. Linux can also use Samba (as can other Unices) to connect to Windows file-sharing or to allow Windows machines to connect to it.