In real life, a material is the stuff something is made of. Rock, brick, sand, knitted red wool, thin leaded glass, anything. Real life materials not only have a look, they also have a feel, a smell, and a response to our actions determined by a weight, flexibility, and the like.
In virtual life, like a Poser scene, a shader refers to a set of object (surface) properties that mimics the looks of a real life material, when rendered. So we can have a rock shader, a knitted red wool shader, etcetera. Shaders do not have a feel, or a smell, they’re inside the computer. But since everyone can tell real life from virtual, the word “material” is also used in these cases, at least in some software communities. So, in Poser one has a Material Room, to make a “brick material” and to assign it to a wall in the Poser scene. In Poser communities, “shader” is rarely used.
In real life, texture relates to the feel of the thing at hand. The surface roughness of the brick when I rub it with my hand, the structure of the fish I feel with my tongue when tasting it. In virtual life however, texture usually refers to the colors of an object surface. A texture then is an image used to assign such colors to elements in my Poser scene. However, since people are somewhat relaxed in their choice of words, they’re happy to assign a “brick texture” to a wall; not only implying color but roughness and reflectivity as well. So in those cases texture means material means shader.
While texture usually refers to an image which is used to assign colors to a surface(property), a map refers to an image which is used to vary the amount of something. A bump map to vary the amount of roughness, a transparency map to vary the opaqueness, and so on. Maps in those cases tend to be black & white, which refer to 0% .. 100% and have greyscales for everything in between.
On the other hand, mapping (as in: UV-mapping) is the term for assigning images in general to an object surface whether it’s for coloring or for determining roughness or reflectivity. So some people might use “map” while referring to the image driving the coloring process too. Fortunately, there is some method in this madness: as shader is hardly used in the Poser community, material or texture is used instead. The people using material for the whole thing tend to use texture for the coloring images. The people using texture for the whole thing tend to use texture-map for the images. But be aware; without context or background info, “brick texture” still might mean either the whole thing or just the color-driving image.