IList<Type> to IList<BaseType>

Use IEnumerable<T>.Cast :

IList<Vehicle> vehicles = cars.Cast<Vehicle>().ToList();

Alternatively, you may be able to avoid the conversion to List depending on how you wish to process the source car list.

That sort of polymorphism that lets you cast IList<Car> to IList<Vehicle> is unsafe, because it would let you insert a Truck in your IList<Car>.

You're facing the problem that there is limited co- and contravariance in C#. There is an interesting approach in C# 4.0, described here at the very ending. However, it creates some other limitations that are related to the truck-problem in the answer from Novelocrat.