3D Textures & Shaders: 

Firstly, I'll try to explain what the difference between the two is. 

A texture is an image that you put onto a 3D model's surface, to make it look like it has texture.

 It gives the model its colour and realistic quality. 

(Kumar, n.d.)

Like the picture above, a texture has been applied to a cube, in order to make it look like a wooden crate. Textures can be created in many different programs, and add realness to your 3D models. 

Now, a shader is a set of properties that you apply to an object, which determine things such as light reflection, light absorbency, translucency, glow, shine, etc. You can then apply textures to the shader, so that it has all the properties you just set for that shader.

Below are some examples shaders...

In some programs, there isn't actually a distinct difference between the two, but this is the difference I have learned about thus far. 

For working in the 3D Graphics industry, this knowledge is incredibly important. It's useful to know which is which, and exactly how both textures and shaders affect a 3D object.
To be able to use this to make incredibly realistic in games is awesome, and I appreciate the work that texture artists put in all the more.
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References:

3dbuzz.com,. (2004). what is the difference between shaders and textures?. Retrieved 1 July 2014, from http://www.3dbuzz.com/forum/threads/58012-what-is-the-difference-between-shaders-and-textures

Create 3D Games,. (2012). Shaders, Materials, and Textures. Retrieved 1 July 2014, from http://create3dgames.wordpress.com/2012/07/24/shaders-materials-and-textures/

Kumar, K. (n.d.). K.S.Satish Kumar Portfolio: Texturing A Mapped Model. Satish3dartist.blogspot.com.au. Retrieved 1 July 2014, from http://satish3dartist.blogspot.com.au/2010/08/texturing-mapped-model.html

Wiki.blender.org,. (n.d.). Retrieved 1 July 2014, from http://wiki.blender.org/uploads/thumb/3/30/Manual-2.5-Material-Shader-Lambert.png/320px-Manual-2.5-Material-Shader-Lambert.png