Sphagnum is a family of moss which has typically large cell structures enabling them to absorb large amounts of air and water in a way very similar to a sponge. A peat bog is an area of moss wetland wherein, over generations, the moss dies and is overgrown by new shoots. The underlying material, which is called the peat, slowly decomposes and in so doing actually supports the overgrowth. These boglands are harvested for the layers of this partially decomposed plant material. The Canadians have millions of acres of this type of wetland so they sell quite a bit of it. As far as I can tell there ought not to be much of a difference between these two terms, unless of course the peat in question is from a type of moss that is not of the sphagnum variety.
For our purposes, the decomposing organic material basically releases carbohydrates which is in a form that is accessible to the bacteria. The sediment bacteria require all the same things that plants and animals require for growth. Carbon, NPK and micronutrients are all necessary for healthy bacteria, so if the sediment is rich in accessible forms of these components then both plant roots and bacteria can benefit. Accelerating the bacterial colonies stabilizes the tanks chemistry helping to fix Nitrogen more quickly, and in so doing reduces the level of ammonium. Sediment bacteria do exactly the same job as the filter bacteria, so it's in our interest to help this process along.
I believe that the more exotic sediments such as AquaSoil have peat baked on to the surface of the clay granules in addition to NPK. Many of the sediment supplements (which require topping) such as the JBL and the Tropica product are basically peat derived, either in a mushy form or dried on clay pellets. I'm less certain of their NPK content though. Anyway, that's why the supplements have to be topped, so that they don't make a mess as they decompose. In James' Akadama journal you can see that he is basically simulating Aquasoil by adding the ingredients that do the same job as the industrially fabricated product (for a much lower price).
Cheers,