Well you say 10 speed bike. But unlike the old days, you seem to be simply adding the front two sprockets to the rear eight sprockets. BITD, we use to multiply those two numbers.
However for the last 25 years and even into the previous century, most experienced with cycling will only refer to a bikes speeds as the number of sprockets on the rear. Unless of course it's a IGH hub and you only see the one external sprocket.
Though confusingly some cheap bike manufacturers and retailers of cheap things still refer to them by the rear and front multiplied together. Don't be one of them!
The picture of the wheel you show is a bad angle and fuzzy. I only count 9 sprockets on it. You say you have Chorus 8. So you should be looking for a wheel with 8 sprockets on the rear. And preferably, IMO, they should be a Campagnolo free hub and Campagnolo cassette. Though again, you can use a wheel that has a Shimano/SRAM compatible free hub and cassette.
Typically new wheels don't come with a cassette on them. You should know what this wheel has on it in your picture. The cassette from your existing wheel might be able to go on it. But not if one is Campagnolo and the other Shimano/SRAM. In many instances, Shimano free hubs can deal with cassettes of one or two more sprockets or less sprockets. Campy probably does too. But I don't know for certain.
For issues that deal with mechanical stuff of your bicycle, the
Bicycle Mechanics is a better place to post those type questions. You'll get more notice from those that do know and less from those that don't know for certain.... which is me.