I\'ve started learning about Microsoft Azure last year and one of the services provided was the Cloud Services. The way I understand Cloud Services is that it is a service m
There has been a bit of movement in the last month :). Web Sites have become Web Apps. Same thing with Mobile Apps.
Now to answer your question on the contrast between the two, each serves their own goal. Cloud Services was your PaaS related for a VM. On the other hand, App Services speaks to "resourcing groups."
With regards to the App Services, you are able to condense a lot more applications within instances of a VM, without much effort. However, the biggest seller that the App Services have over Cloud Services is the ability to compose business processes with the App Logic, much like BizTalk does the external connecting to other processes.
The resourcing groups is the next phase on how to approach DevOps. IMHO, the next move that Azure would 'promise' is the notion that your applications are deployed as microservices on the Microsoft Service Fabric. (It was just announced last week).