My oldest just turned 18 and we are all traveling together as a family.. She will be graduated from high school and has been accepted to a university. Would a student card get her discounts? Do my teenage boys (13 and 15) need a youth card?
Get her discounts to what? Movies, restaurants, etc. Who knows? You'd have to check any place that you plan to visit to see if the cards you mention are worth getting. At the Eiffel Tower, there is a reduced price for those who are 12 to 24 -- no youth card needed. There is free admission at museums for those under 18 and no one asked me for ID when my daughter was 16 and all of 6 feet tall but if they do ask, all you need is proof of age. Now that your oldest is an adult (or at least over 18), she is no longer eligible for under 18 free entry and the reduction in price at museums for those under 25 is available only for those who are citizens or long-term residents of an EU member state.
www.isic.org has a discount search function that collaborates the reply above, though not in the clearest way.
It does reveal some museums with a "Student" discount, such as the Musee des Beaux Arts in Reims, where the card works to prove student status.
But it does NOT help you with those museums, such as the Louvre, which specify only age-based discounts. The fact that the site mentions these at all is misleading, at least for the uninitiated. A passport or European ID card is the only proof of age required at those locations.
In most of Europe no one cares if someone is a student; these reductions are based on age and at 18 she will not qualify for many. One age based reduction it the transport ticket jeune -- this is a one day pass like the Mobilis Pass which covers what ever zones you pay for and is about 60% of the cost of the Mobilis. People 4-25 can buy these for travel on Sat or Sunday. The Eiffel Tower has a cheaper ticket for young people. None of the museums do; 17 and under are free and EU residents 25 and under are free. The Louvre is free Friday nights to young people of any nationality.
Is the University in France? If so she would be a French resident and able to receive the discounts
When our (U.S. citizen) son was a student at an EU university (full-time, not visiting), and had a student visa, he was able to get free student entries at museums. But that's because he was a legal resident of the UK at the time. If that is your daughter's situation, then yes she can get discounts / free entries. My son needed both his student ID and his passport and student visa to be able to get the free entries.
My college aged kids were able to get some student discounts with the college IDs at some places in Europe. I recall looking into an ISIC card and abandoned the idea. When traveling, we never saw a place to use it that wouldn't except a college ID.