There is no such thing as a “cart template” per se. You can create different Album Templates that are cart enabled. Each of these can have slightly different settings, found in the Cart add-on for the respective album template.
When you create the albums, they can be assigned different pricing schemes
But the payment and tax options in the Cart Settings are global, meaning they apply to all transactions and all cart-enabled albums.
If you need different tax options for different types of customers, the only way I can think of doing that is by having two different carts. And to do that, you’d need two different sites, each with their own Backlight installation. This is pretty easy to do using subdomains, if that’s an option for you.
You could have one site for regular customers and another for school photo clients. Then you can customize the Cart settings for each.