OpenGL is a library a bit special. Most of the features are provided first through "extensions", and then the extensions are integrated in the core version of OpenGL.
On Windows, Microsoft provides an implementation of OpenGL which is very old (1. something).
If you use Windows, the only thing you will get when you install Visual Studio (or MinGW, MinGW-TDM etc) are Opengl headers for the 1.x version with the OpenGL library.
That doesn't mean you are stuck with this antic API however: you can tap in the new features thanks to the extensions. Some libraries like GLEW (google it), or GLXW make it easier to use those extensions.
look for GLEW or GLXW.
Hope it helps
An OpenGL implementation is usually provided with the graphics card driver installation. However, in order to use the vendor provided GL implementation, you usually have to link to a stub implementation. On Linux this is usually libGL.so and on Windows its opengl32.lib( GL calls are forwarded to the correct implementation at runtime provided the appropriate context is created ). For Windows, opengl32.lib is provide with the platform/windows SDK or the compiler installation. There is not specific headers for ATI/Nvidia or any other vendor. The latest headers are provided on the OpenGL website and the libraries are OS dependent and provided by the respective platforms.
Your understanding of OpenGL API implementation is correct.
Implementation of API differs among graphics vendors but header is same across all the vendors. That means, the header can be found on OpenGL website, but the API implementation should be downloaded from vendor site, which comes with graphics driver.
For example, if the machine has only AMD graphics, then you should download graphics driver from AMD site. If there is graphics from another vendor (Intel integrated or an NV board), then you should download their graphics driver too. The application links against "opengl32.dll" which is part of OS. That dll determines from DC of target window which driver should be responsible for rendering to it and loads that. This is the ICD mechanism.
The latest AMD driver supports OpenGL 4.4.