From what I noticed, they do pretty much the same thing, provide services in form of IoC/DI. However, IAmbientServices has a member of type ICompositionContext. I don't really get the difference between the two of them and why are they aggregated this way?
The concise answer is: the ambient services contain services registered before the IoC/DI/composition container is built, while the composition context is the root container for the IoC/DI, and itself is a service registered into the ambient services.
As a side note, all the services registered in the ambient services are later registered automatically also in the DI container, including IAmbientServices, so they are available for composition, too.
Examples for ambient services:
As a general rule of thumb, prefer using services registered in the DI container, you will need very rarely ambient services.