Do I need to tell them what countries I will be visiting? Are the rules different depending on where I intend to travel?

Travelling to EU member states only – the Green Card document itself is designed so it can be used in the same way across every EU member state. The Green Card will specify which countries you are allowed to drive in. Under the current rules, it will always cover you for each EU member state. However, your insurer may still ask you to confirm which countries you intend to travel to.   

If travelling to a Green Card country that is not an EU member state then  you will need to inform your insurer which countries you will be visiting as you will not be automatically be covered for driving in any country outside the EU, even if they are part of the Green Card system.