Yes, you got the right idea. AFAIK every type of code running on the GPU is called a shader (eg. special data operations are even called "compute shaders", although they are a different beast). All the operations you mentioned (colors, shadows, shading, image-effects, general image-processing) are achieved through parallelized computing combining lots of data arrays (vertices and their properties, source textures, pre-computed functions, target textures, buffers, etc).
For example, to get light and shadows, your shader should have access to some (probably global) variable about the position and direction of eg. a spotlight. Very often composite lighthing is achieved by combining multiple shader passes (a base pass for global ilumination, and one for each light for example), each literally adding more light (additive pass). Now, in order to avoid adding light for pixels where the light source is blocked (ie. shadow) the most common technique is using what's called a Z-buffer (just a floating point texture). You want to know for each light in the scene where their light reaches, so (before all lighting is applied) you set up a single shader pass that combines all solid geometry on the scene and using the light position and direction as the camera transform, and use a special shader whose only purpose is writing the objects distance to the Z-buffer. Now, every time you want to know whether a point in space is reached by your light, you go about sampling this Z-buffer (after doing some geometry) and compare the point's distance to the saved value in that direction. Yes, it can be very buggy and precision errors abound, and every engine worth their salt already does this for you, but lets you get in there and modify the process.
Everything else are variations on this theme. Deferred rendering is rendering data instead of colors into an intermediate texture which is later processed to get the colors. Blur effects are 2D convolutions of the rendertexture (eg by a Gaussing kernel). Tesseletion shaders are about generation new geometry in the vertext shader. Even drawing text is achieved through font atlasing and small rectangles.
For example, to get light and shadows, your shader should have access to some (probably global) variable about the position and direction of eg. a spotlight. Very often composite lighthing is achieved by combining multiple shader passes (a base pass for global ilumination, and one for each light for example), each literally adding more light (additive pass). Now, in order to avoid adding light for pixels where the light source is blocked (ie. shadow) the most common technique is using what's called a Z-buffer (just a floating point texture). You want to know for each light in the scene where their light reaches, so (before all lighting is applied) you set up a single shader pass that combines all solid geometry on the scene and using the light position and direction as the camera transform, and use a special shader whose only purpose is writing the objects distance to the Z-buffer. Now, every time you want to know whether a point in space is reached by your light, you go about sampling this Z-buffer (after doing some geometry) and compare the point's distance to the saved value in that direction. Yes, it can be very buggy and precision errors abound, and every engine worth their salt already does this for you, but lets you get in there and modify the process.
Everything else are variations on this theme. Deferred rendering is rendering data instead of colors into an intermediate texture which is later processed to get the colors. Blur effects are 2D convolutions of the rendertexture (eg by a Gaussing kernel). Tesseletion shaders are about generation new geometry in the vertext shader. Even drawing text is achieved through font atlasing and small rectangles.