Jo is basically correct in his answers, but I'd like to add a few things. (I assume you are talking mostly about countertops, so I'll address my responses to that market.)
Sealers are used primarily to impart water resistance (and also impart, somewhat, dirt and stain resistance) to stone and concrete surfaces. They may or may not add sheen--depends on the sealer.
Waxes, on the other hand, DO add sheen (or makes them "luminous", as your reader says). That is their primary use. They also give some slip properties, and water resistance--although the waxes wear away quickly, whereas the sealers last for many months. Waxes aren't used much at all on countertops, mostly on floors...
"Glue is glue"?!?! How insulting, Jo! Seriously--glue/adhesive is used to laminate the edges on countertops, repair cracks, replace broken pieces, filling chips, gluing the seams together, reinforcing (rodding and/or mesh attachment), and setting countertops. Most quality adhesives are epoxy-based.
"Resin" can mean almost anything. All polymers are basically resins--this includes acrylics, epoxies, polyesters, urethanes, etc. In the context of countertops, however, "resin" usually refers to the product applied to the slab by the quarrier, in the form of a coating that is flooded onto the slab. This coating is cured, then the slab is polished, yielding a very non-porous "resinated" slab that is very good for water-resistance and somewhat-improved stain resistance. The "resin" used is usually a polyester, but sometimes acrylics or epoxies are used. While resinating does make the slab less porous (by filling all the surface micropores), it casues some potential problems: it adds cost; it sometimes adds color; it makes it very difficult to color-match any sawed edges (since only the surface is resinated, a freshly-sawed edge does not have any resin on it); and the resin can sometimes discolor in sunlight changing the color of the slab. I, personally, would not have a resinated slab in my kitchen.
Hope this helps, let me know if you have any more questions.
Mike Beckmann
Bonstone Materials Corp.
Concrete Repair and Adhesives - Bonstone