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@Sam Hobbs how to host asp.net website on cloud
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The term cloud can mean many things. It could mean that a database is somewhere else from where that application executes. That technology began as Distributed Databases about half a century ago.
A cloud could be something that executes a program in a system separate from the user of the program. Server-side internet applications are examples of that. I think that ASP.Net is like that. As best as I understand things, ASP.Net applications are usually hosted in a cloud. Azure is one of many possible clouds for that.
If you are asking how to use a database that is in a different system than the system executing an ASP.Net application then I think it is basically a matter of specifying an appropriate connection string for the cloud database.