Google App Engine vs Google Cloud Platform

Google App Engine
Google App Engine lets you run web applications on Google's infrastructure. App Engine applications are easy to build, easy to maintain, and easy to scale as your traffic and data storage needs grow. With App Engine, there are no servers to maintain: You just upload your application, and it's ready to serve your users.
Google Cloud Platform
Google Cloud Platform is a set of modular cloud-based services that allow you to create anything from simple websites to complex applications. Cloud Platform provides the building blocks so you can quickly develop everything from simple websites to complex applications. Explore how you can make Cloud Platform work for you.
Google Cloud Platform has better video than Google App Engine

2015 - Google launched custom machine types for its Cloud Platform

Google Cloud Platform launched a new way of buying virtual machines in its cloud - Custom Machine Types. With new Custom Machine Types, Google lets you specify exactly how many vCPUs (up to 32) and how much memory you need (up to 6.5 GiB per vCPU — Google likes to be precise, so it doesn’t use ‘gigabyte’ and instead specifies the number of gibibytes). If your needs change — as they inevitably will — you can adjust the number of cores and memory as needed. Maybe you’ve outgrown the virtual machine with two vCPUs. Typically, you would have to step up to a machine type with four vCPUs, even if you only needed three. Because you don’t have a choice, you end up paying for more power than you need.