The new 9-speed right hand shifter will say 9-speed on it. I think that's the difference. Have a look at these spare parts docs on the Campagnolo site, they may help.
The 2001 document explains the compatibility (or lack of it) on page 30.
They can be up or downgraded with a small spare part. I've got some old Athena shifters and it wasn't until I measured the cable pull that I realised a previous owner had upgraded them to new style internals.
Sounds like it. If you need to double check, it's measurable - 1.6mm of difference over 8 clicks. It's easier if it's on a bike, you can hold a ruler next to the downtube, put a bit of tape around the cable and see how far it moves.