You are confusing a few concepts here. Just because a version is released later, it do not mean it has more features. .NET Core 1.0 ist an LTS release and will be supplied with updates for 2 or 3 years iirc.
So even after 1.1 gets released, there will be maintenance for 1.0 which fix bugs or security issues. This has always been the case in Software development, look at Java. When Java 1.8 got released, there were still updates for Java 1.7.
The .NET Core SDK contains the dotnet cli tools, used to restore the packages, build, deploy and run .NET Core applications and it also contains the .NET Core runtime, which provides the framework DLLs (like .NET Framework 4.x setup) which you need to run portable apps.
The .NET Core runtime/SDK are independent of the CLI tools and can also be obtained via nuget packages.
The .NET Core Tools for Visual Studio 2015/2017 are just a set of tools which allow Visual Studio add support to the new project types and build pipeline.
The .NET Core Tools for VS also contain the SDK/runtime.
What you need to run on Azure, depends on your needs and which kind of runtime is installed on the Azure App Service instances, as they usually lag a bit behind the regular releases.
i.e. if you create self-contained applications, which get deployed with the .NET Core runtime, then you can just use any version, as each application will have its own runtime which can run side-by-side.
If you want run portable applications (which ship w/o .NET Core framework libraries when deployed), then you need to have the correct runtime installed on Azure App Service (Azure blog usually posts when new runtimes become available).
All other depends on your development environment.
TL;DR:
If you
- use Visual Studio 2015: Install Visual Studio 2015 Tools (Preview 2) *
- use Visual Studio 2017: Download Visual Studio 2017
- don’t use Visual Studio, but want to develop for/with .NET Core: Install .NET Core SDK
- don’t use Visual Studio, but want to run .NET Core Appl: Install .NET Core Runtime
or
- .NET Core Runtime (1.0.x or 1.1.x): Just the runtime
- dotnet-cli: Just build/deployment tools
- .NET Core SDK: Runtime + dotnet-cli
- .NET Core Tools for Visual Studio: Runtime + dotnet-cli + Visual Studio integration (and new project templates)
cli-tools and Visual Studio Tools are not finished yet, hence in preview. They should go RTM together with VS2017 and the new MSBuild based project structure (moving away from xproj to csproj files), but this do not effect the status of the runtime/SDK.