Windows Azure - IaaS VS PaaS

Windows Azure offers multiple categories but we will go through just a couple of them.

Infrastructure as a Service (IaaS) and Platform as a Service (PaaS)

Windows Azure - IaaS Support

This technology lets you create and use Virtual Machines in the cloud.
VM in Azure has an operating system, storage and networking capabilities and can run a wide variety of applications. You can use an image provided by Azure or one of its partners, or use your own.
Virtual machines use virtual hard disks (VHDs) to store their operating system (OS) and data. VHDs are also used for the images you can choose from to install an OS. The following figure shows this, as well as two of the tools for creating and managing your VMs.

VMs can be managed using a browser-based portal, command-line tools with support for scripting, or directly through the REST API.

Windows Azure - PaaS Support

This technology is designed to support applications that are scalable, reliable, and cheap to operate.
Just like App Services are hosted on VMs, so are Cloud Services, however, you have more control over the VMs. You can install your own software on Cloud Service VMs and you can remote into them.
More control also means less ease of use; unless you need the additional control options. It's typically quicker and easier to get a web application up and running in Web Apps in App Service compared to Cloud Services.

Scaling and management

With Cloud Services, you don't create virtual machines. Instead, you provide a configuration file that tells Azure how many of each you'd like, such as three web role instances and two worker role instances, and the platform creates them for you.
You can choose what size those backing VMs should be, but you don't explicitly create them yourself. If your application needs to handle a greater load, you can ask for more VMs, and Azure will create those instances.
If the load decreases, you can shut those instances down and stop paying for them.
Cloud Services also provide monitoring. Like Azure Virtual Machines, it will detect a failed physical server and restart the VMs that were running on that server on a new machine.
But Cloud Services also detect failed VMs and applications, not just hardware failures.
Unlike Virtual Machines, it has an agent inside each web and worker role, and so it's able to start new VMs and application instances when failures occur.
If you need control over the web server environment, such as the ability to remote into your server or configure server startup tasks, Azure Cloud Services is typically the best option.
If you have an existing application that would require substantial modifications to run in Azure Websites or Azure Cloud Services, you could choose Azure Virtual Machines in order to simplify migrating to the cloud.
However, correctly configuring, securing, and maintaining VMs requires much more time and IT expertise compared to Azure Websites and Cloud Services.
If you are considering Azure Virtual Machines, make sure you take into account the ongoing maintenance effort required to patch, update, and manage your VM environment.

Monitoring

Cloud Services also provide monitoring. Like Azure Virtual Machines, it will detect a failed physical server and restart the VMs that were running on that server on a new machine.
But Cloud Services also detect failed VMs and applications, not just hardware failures.
Unlike Virtual Machines, it has an agent inside each web and worker role, and so it's able to start new VMs and application instances when failures occur.

What should I use? Making a choice

If you need control over the web server environment, such as the ability to remote into your server or configure server startup tasks, Azure Cloud Services is typically the best option.
If you have an existing application that would require substantial modifications to run in Azure Websites or Azure Cloud Services, you could choose Azure Virtual Machines in order to simplify migrating to the cloud.
However, correctly configuring, securing, and maintaining VMs requires much more time and IT expertise compared to Azure Websites and Cloud Services.
If you are considering Azure Virtual Machines, make sure you take into account the ongoing maintenance effort required to patch, update, and manage your VM environment.