There might be exceptions, but for reference types the new-keyword usually creates an object in an internal data structure called "heap". The heap is managed by the CLR (Common Language Runtime). It makes no difference whether you have a static or instance member or a local variable.
The difference between static members and instance members (the ones without the keyword static) is, that static members exist only once per type (class, struct) and instance members exist once per instance (per object).
It is only the reference which is static or not; this distinction does not apply to the referenced object (unless the object is a value type). A static member, an instance member and a local variable can all reference the same object.