This article is a bit of history about the various Microsoft HTTP client stacks.
WININET
Originally, there was one - the WININET implementation, that was written for the Internet Explorer browser. The implementation for this was encapsulated in Wininet.dll. In it's original implementation (as shipped in IE 2.0/IE 3.0/IE 4.x), it supported the following protocols - HTTP, FTP, GOPHER. It also supported HTTP caching. For more information, see WININET Msdn Page
As client side HTTP stacks stood in those days, it was pretty good and usable. While it was originally targetted for Internet Explorer, a lot of third party applications began to be built around it. And as frequently happens, it was being put to uses for which it was not intended.
For eg, a lot of customers started using it for implementing Middle-tier applications, where the DLL was loaded in an ISAPI in the IIS process. Wininet was not really intended for such uses - it was heavily bound to a user context because of it's dependency on the user directories for storing the cached web pages. Also, it did not support delegated authentication. Also, some of the Wininet settings were only configurable through the IE interface.
Wininet still lives on - it is the HTTP stack being used by the Internet Explorer browser. In OS Versions from Windows7 onwards, it might have been replaced by WebIO.
WinHTTP
More and more customers were using Wininet in a non user-context - for eg, in middle-tier apps, and it was not working very well. As I mentioned above, Wininet was not designed to be used in a server environment. So, a separate team was spun off to come up with a solution for that.
The result of that was WinHTTP. This was a standalone DLL, that borrowed heavily from Wininet in terms of the interfaces it offered. However, it was designed to be usable in server applications as well. It was a robust implementation, that exposed it's functionality through exported functions, as well as a COM interface that could be used in a server scenario.
However, it was a subset of the Wininet implementation. It did not support cookies, caching, and automatic credential handling. Also, Wininet had a lot of code to handle buggy HTTP servers, and proxy servers, and that code was not supported by WinHTTP.
There were two version of WinHTTP. WinHTTP 5.0 was a redistributable version, and was downloadable as a standalong component from Microsoft. WinHTTP 5.1 was made a part of the operating system, and thus was not downloadable as a separate component.
System.Net
As part of Microsoft's effort to build a clean-room, managed execution environment like Java, a separate team was staffed to develop the networking library for the managed frameworks that were to ship as part of this. It was part of the project Codenamed Lightning.
The networking classes were encapsulated in the System.Net namespace. This team was staffed by ex-WININET developers, and led by Henry Sanders who is now a Vice President at Microsoft.
This library was written with a view to fix some of the problems with WININET. It was designed from the ground up to be usable in middle-tier scenarios. Also, it was designed to support asynchronous networking calls. Even the sync networking calls ended up calling the async implementations underneath, which caused the application to use up an extra Thread. This was later fixed in .Net Framework 2.0 (codename Whidbey). Also, it supported asynchronous operations on both WinNT and Win9x platforms, whereby it used Completion ports on WinNT, and Overlapped I/O on Win9x.
The class design (for the Http client stack) in the System.Net library is such that it support both beginners and advanced users seamlessly. For beginners, System.Net.WebClient offers an easy to use API to get web resources, and even to send POST requests to Web forms. For advanced and fine grained control, System.Net.HttpWebRequest class is the recommended entry point.
With a new design philosophy, the API designers decided to make usage consistent with other parts of the framework. For eg, doing asynchronous network I/O in Http was the same pattern as doing asynchronous I/O on a File handle in the System.IO.File class.
One extra thing that was available in System.Net, was a Socket implementation, similar to the facilities provided by Windows Sockets (Winsock) library on Windows. Again, keeping in mind the overall design philosophy of the .NET framework, later releases added Stream implementation ( for eg SSLStream) that could be hooked up to a Socket to provide higher level network stack functions, like encryption, authentication etc.
For debugging a Tracing/Logging functionality is provided that allows most network I/O to be logged using the .NET Runtimes logging functionality.
WebIO
In Windows7, a new native HTTP stack was written, called WebIO. This is not documented as a public API, and is internal only to the browser and the Operating System.
Conclusion
For developers who are using .NET, the primary and only choice for a HTTP client library is System.Net namespace. However, for use outside of the .NET Runtime, the options are Wininet and WinHTTP. All three of these stacks should support most modern applications to varying degrees.