I've always found this very confusing. There is a WindowsAzure.Storage Nuget package authored by Microsoft which allows you to work with, for example, blob storage (creating blobs, etc.). There are also Microsoft.Azure.Storage.* packages which accomplish the same thing, also authored by Microsoft. If your project happens to have dependencies on both, you can have naming conflicts e.g. (The type 'CloudStorageAccount' exists in both 'Microsoft.Azure.Storage.Common, ... and 'Microsoft.WindowsAzure.Storage, ...).
Here are links to the two alternatives:
https://docs.microsoft.com/en-us/dotnet/api/overview/azure/storage?view=azure-dotnet
https://github.com/Azure/azure-storage-net/blob/master/README.md
What is the difference and when would I be motivated to use one over the other?