Can I use Thunderbolt to Thunderbolt cable to copy from one macbook air to another?

Of course, but you will have to start one of the Macs into Target Disk Mode, pressing T key while the Mac is starting with the Thunderbolt cable connected, so the MacBook Air in Target Disk Mode will appear on the Finder sidebar of the other Mac as an external disk, so you can copy and transfer files from and to it

davka25 wrote:

Thank you.

Will a Firewire cable do the same?

Since Macbook Air's lack a Firewire port, no.

You don't need to use Target Disk Mode. Use Thunderbolt Bridge (e.g. on OS X Mavericks 10.9.1). For details, find my solution at https://discussions.apple.com/thread/5860467.