They're all individually and together a texture. A texture is just surface detail, normals, AO, and diffuse all provide surface detail. When combined you get a complete surface detail. Originally, diffuse was the only form of applying texture, by changing the color of the pixels of the rendered polygons.
A texture has always meant a bitmap, when talking with other game artists. Shader is the code which controls how those textures are applied to the model, what kind of user-adjustable settings are available for the surface, what kind of specular equation is allowed, etc. Material is the settings you can adjust for a…
Let's not forget there's 'texture' as in the surface property of an object, as in 'The texture of the rubber ball is rough but soft' or 'His chin had a rough texture by the end of the day.' I've also seen texture used as a non-pattern overlay, as in images you'd download from cgtextures, the more generalized form of a…