Card with 10 tickets. What is it called?
The French word carnet is used in English public transport networks for a ticket (or a book of tickets) which can be used on more than one journey.
Pronunciation: /ˈkɑːneɪ/
- A book of tickets for use on public transport in some countries.
ODO
Carnet tickets
If you travel regularly to and from London but not often enough to buy a Season ticket, the Carnet ticket booklet could save you time and money.
You can buy a Carnet booklet of either five or 10 single journey tickets and you’ll save 10%. Your Carnet tickets will need to be used within three months and only from selected stations. Don’t forget that Carnet tickets are one-way, so you’ll need a separate book of Carnet tickets for your return journeys.
There are two types of Carnet tickets to choose from:
Anytime tickets - unrestricted travel
Off-Peak tickets - choose this if you:
- Arrive in London after 10:00 Monday to Friday
- Leave London after 09:30 Monday to Friday
- Travel before 16:30 and after 19:01 Monday to Friday
- Travel on public holidays
Please note that Carnet booklets are only available as Standard Class fares.
Thameslink Railway
If it's a solitary card from which 10 uses is used and somehow marred/marked, then calling it a punch card in the USA is easily understood, even if physical "punches" aren't used.
A good alternative could be called a Voucher Card. I can't speak for English usage for slang/jargon outside the USA though.