Baggage on Vueling: Madrid to Rome

Got a baggage question. I'm buying 2 tickets from Madrid to Rome online with Vueling. They charge 20e per suitcase. We only plan on taking one carryone for both of us. Does my carryone count as a 20e suitcase?

Thanks!

8.6 Hand luggage Each passenger may carry one (1) piece of hand luggage with a maximum weight of 10 kg, the dimensions of which do not exceed 55x40x20 cm.
At the loading gate, hand luggage that does not comply with the Company’s regulations – that is, it exceeds the stipulated quantity, weight and/or measurements (55x40x20) – will be withdrawn and loaded into the aircraft hold, at an additional cost.
Furthermore, each Passenger can transport onboard, in their own care and at no extra cost:

A handbag or small wallet.
A coat or travel rug.
A walking stick.
A pair of crutches.
A small camera or video camera or binoculars.
A laptop computer.

Which is quite generous compaired with some UK airlines !!!

Thanks Jan!

Speaking of UK airlines, I ended booking my flight to Rome with Easyjet as the time table worked better for us.

Be aware, Easyjets hand luggage is restricted to 1 piece per person.( laptops, purses etc must go in the 1 bag!!)
maximum size 56 x 45 x 25. There is no weight limit, but you must be able to put your own bag in the overhead.

usually they all similiar Easyjet, ryanair, vuelings, low carrier, heavey restrictions, charge for many extras but in the end cheaper than regular carrier and longer hauls for on land travel.
the carry on board bag with size, weight limitations is free, the check in bags are charge. The airline websites have all the information.